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The passage around this formula

It helps to write the whole loop down once, because the assumption buried in it is the one the rest of this article is about: $a_t = \pi_\theta(h_t \mid \mathcal{T}_t), \qquad o_t = \mathrm{Call}(a_t), \qquad h_{t+1} = h_t \oplus (a_t,\, o_t)$. Here $\mathcal{T}_t$ is the tool set most recently returned by tools/list , each member carrying its own schema; $\pi_\theta$ is the model, which is expected — but not forced by anything outside its own training — to emit a call $a_t$ whose name and arguments validate against some tool in $\mathcal{T}_t$ ; $\mathrm{Call}$ is dispatch through the client to the server and back, exactly as described above; and $h_{t+1}$ is the context the model reasons over on the next step, built by appending the call and its result to what came before. The assumption is in…

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