diff --git a/Project.toml b/Project.toml
index 201c4e7370..0f232dc90d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -54,7 +54,7 @@ AbstractPPL = "0.11, 0.12"
 Accessors = "0.1"
 AdvancedHMC = "0.3.0, 0.4.0, 0.5.2, 0.6, 0.7, 0.8"
 AdvancedMH = "0.8"
-AdvancedPS = "0.6.0"
+AdvancedPS = "0.7"
 AdvancedVI = "0.4"
 BangBang = "0.4.2"
 Bijectors = "0.14, 0.15"
@@ -67,7 +67,7 @@ DynamicHMC = "3.4"
 DynamicPPL = "0.36.3"
 EllipticalSliceSampling = "0.5, 1, 2"
 ForwardDiff = "0.10.3, 1"
-Libtask = "0.8.8"
+Libtask = "0.9.3"
 LinearAlgebra = "1"
 LogDensityProblems = "2"
 MCMCChains = "5, 6, 7"
@@ -85,7 +85,7 @@ Statistics = "1.6"
 StatsAPI = "1.6"
 StatsBase = "0.32, 0.33, 0.34"
 StatsFuns = "0.8, 0.9, 1"
-julia = "1.10.2"
+julia = "1.10.8"
 
 [extras]
 DynamicHMC = "bbc10e6e-7c05-544b-b16e-64fede858acb"
diff --git a/src/mcmc/particle_mcmc.jl b/src/mcmc/particle_mcmc.jl
index ffc1019519..a81f436c87 100644
--- a/src/mcmc/particle_mcmc.jl
+++ b/src/mcmc/particle_mcmc.jl
@@ -25,9 +25,8 @@ function TracedModel(
             "Sampling with `$(sampler.alg)` does not support models with keyword arguments. See issue #2007 for more details.",
         )
     end
-    return TracedModel{AbstractSampler,AbstractVarInfo,Model,Tuple}(
-        model, sampler, varinfo, (model.f, args...)
-    )
+    evaluator = (model.f, args...)
+    return TracedModel(model, sampler, varinfo, evaluator)
 end
 
 function AdvancedPS.advance!(
@@ -59,20 +58,10 @@ function AdvancedPS.reset_logprob!(trace::TracedModel)
     return trace
 end
 
-function AdvancedPS.update_rng!(
-    trace::AdvancedPS.Trace{<:AdvancedPS.LibtaskModel{<:TracedModel}}
-)
-    # Extract the `args`.
-    args = trace.model.ctask.args
-    # From `args`, extract the `SamplingContext`, which contains the RNG.
-    sampling_context = args[3]
-    rng = sampling_context.rng
-    trace.rng = rng
-    return trace
-end
-
-function Libtask.TapedTask(model::TracedModel, ::Random.AbstractRNG, args...; kwargs...) # RNG ?
-    return Libtask.TapedTask(model.evaluator[1], model.evaluator[2:end]...; kwargs...)
+function Libtask.TapedTask(taped_globals, model::TracedModel; kwargs...)
+    return Libtask.TapedTask(
+        taped_globals, model.evaluator[1], model.evaluator[2:end]...; kwargs...
+    )
 end
 
 abstract type ParticleInference <: InferenceAlgorithm end
@@ -402,11 +391,11 @@ end
 
 function trace_local_varinfo_maybe(varinfo)
     try
-        trace = AdvancedPS.current_trace()
-        return trace.model.f.varinfo
+        trace = Libtask.get_taped_globals(Any).other
+        return (trace === nothing ? varinfo : trace.model.f.varinfo)::AbstractVarInfo
     catch e
         # NOTE: this heuristic allows Libtask evaluating a model outside a `Trace`.
-        if e == KeyError(:__trace) || current_task().storage isa Nothing
+        if e == KeyError(:task_variable)
             return varinfo
         else
             rethrow(e)
@@ -416,11 +405,10 @@ end
 
 function trace_local_rng_maybe(rng::Random.AbstractRNG)
     try
-        trace = AdvancedPS.current_trace()
-        return trace.rng
+        return Libtask.get_taped_globals(Any).rng
     catch e
         # NOTE: this heuristic allows Libtask evaluating a model outside a `Trace`.
-        if e == KeyError(:__trace) || current_task().storage isa Nothing
+        if e == KeyError(:task_variable)
             return rng
         else
             rethrow(e)
@@ -481,6 +469,25 @@ function AdvancedPS.Trace(
 
     tmodel = TracedModel(model, sampler, newvarinfo, rng)
     newtrace = AdvancedPS.Trace(tmodel, rng)
-    AdvancedPS.addreference!(newtrace.model.ctask.task, newtrace)
     return newtrace
 end
+
+# We need to tell Libtask which calls may have `produce` calls within them. In practice most
+# of these won't be needed, because of inlining and the fact that `might_produce` is only
+# called on `:invoke` expressions rather than `:call`s, but since those are implementation
+# details of the compiler, we set a bunch of methods as might_produce = true. We start with
+# `acclogp_observe!!` which is what calls `produce` and go up the call stack.
+Libtask.might_produce(::Type{<:Tuple{typeof(DynamicPPL.acclogp_observe!!),Vararg}}) = true
+Libtask.might_produce(::Type{<:Tuple{typeof(DynamicPPL.tilde_observe!!),Vararg}}) = true
+Libtask.might_produce(::Type{<:Tuple{typeof(DynamicPPL.evaluate!!),Vararg}}) = true
+function Libtask.might_produce(
+    ::Type{<:Tuple{typeof(DynamicPPL.evaluate_threadsafe!!),Vararg}}
+)
+    return true
+end
+function Libtask.might_produce(
+    ::Type{<:Tuple{typeof(DynamicPPL.evaluate_threadunsafe!!),Vararg}}
+)
+    return true
+end
+Libtask.might_produce(::Type{<:Tuple{<:DynamicPPL.Model,Vararg}}) = true
diff --git a/test/Project.toml b/test/Project.toml
index ee964817c5..bb49654a10 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -43,7 +43,7 @@ ADTypes = "1"
 AbstractMCMC = "5"
 AbstractPPL = "0.11, 0.12"
 AdvancedMH = "0.6, 0.7, 0.8"
-AdvancedPS = "=0.6.0"
+AdvancedPS = "0.7"
 AdvancedVI = "0.4"
 Aqua = "0.8"
 BangBang = "0.4"
diff --git a/test/essential/container.jl b/test/essential/container.jl
index 1cb790d5ae..cbd7a6fe2b 100644
--- a/test/essential/container.jl
+++ b/test/essential/container.jl
@@ -23,8 +23,8 @@ using Turing
         model = test()
         trace = AdvancedPS.Trace(model, sampler, vi, AdvancedPS.TracedRNG())
 
-        # Make sure we link the traces
-        @test haskey(trace.model.ctask.task.storage, :__trace)
+        # Make sure the backreference from taped_globals to the trace is in place.
+        @test trace.model.ctask.taped_globals.other === trace
 
         res = AdvancedPS.advance!(trace, false)
         @test DynamicPPL.get_num_produce(trace.model.f.varinfo) == 1
diff --git a/test/mcmc/Inference.jl b/test/mcmc/Inference.jl
index a0d4421869..cf528ce517 100644
--- a/test/mcmc/Inference.jl
+++ b/test/mcmc/Inference.jl
@@ -44,13 +44,13 @@ using Turing
             end
 
             # Should also be stable with an explicit RNG
-            seed = 5
-            rng = Random.MersenneTwister(seed)
+            local_seed = 5
+            rng = Random.MersenneTwister(local_seed)
             for sampler in samplers
-                Random.seed!(rng, seed)
+                Random.seed!(rng, local_seed)
                 chain1 = sample(rng, model, sampler, MCMCThreads(), 10, 4)
 
-                Random.seed!(rng, seed)
+                Random.seed!(rng, local_seed)
                 chain2 = sample(rng, model, sampler, MCMCThreads(), 10, 4)
 
                 @test chain1.value == chain2.value
@@ -256,9 +256,9 @@ using Turing
         pg = PG(10)
         gibbs = Gibbs(:p => HMC(0.2, 3), :x => PG(10))
 
-        chn_s = sample(StableRNG(seed), testbb(obs), smc, 200)
-        chn_p = sample(StableRNG(seed), testbb(obs), pg, 200)
-        chn_g = sample(StableRNG(seed), testbb(obs), gibbs, 200)
+        chn_s = sample(StableRNG(seed), testbb(obs), smc, 2_000)
+        chn_p = sample(StableRNG(seed), testbb(obs), pg, 2_000)
+        chn_g = sample(StableRNG(seed), testbb(obs), gibbs, 2_000)
 
         check_numerical(chn_s, [:p], [meanp]; atol=0.05)
         check_numerical(chn_p, [:x], [meanp]; atol=0.1)
@@ -647,7 +647,7 @@ using Turing
         @model function e(x=1.0)
             return x ~ Normal()
         end
-        # Can't test with HMC/NUTS because some AD backends error; see 
+        # Can't test with HMC/NUTS because some AD backends error; see
         # https://github.com/JuliaDiff/DifferentiationInterface.jl/issues/802
         @test sample(e(), IS(), 100) isa MCMCChains.Chains
     end
diff --git a/test/mcmc/ess.jl b/test/mcmc/ess.jl
index 4afeeb9852..e918b3a512 100644
--- a/test/mcmc/ess.jl
+++ b/test/mcmc/ess.jl
@@ -64,7 +64,7 @@ using Turing
                 @varname(mu1) => ESS(),
                 @varname(mu2) => ESS(),
             )
-            chain = sample(StableRNG(seed), MoGtest_default, alg, 2000)
+            chain = sample(StableRNG(seed), MoGtest_default, alg, 5000)
             check_MoGtest_default(chain; atol=0.1)
         end
 
diff --git a/test/mcmc/particle_mcmc.jl b/test/mcmc/particle_mcmc.jl
index 699ee68547..7a2f5fe1c7 100644
--- a/test/mcmc/particle_mcmc.jl
+++ b/test/mcmc/particle_mcmc.jl
@@ -34,6 +34,7 @@ using Turing
 
         tested = sample(normal(), SMC(), 100)
 
+        # TODO(mhauru) This needs an explanation for why it fails.
         # failing test
         @model function fail_smc()
             a ~ Normal(4, 5)