Let $\tau(x)$ be the number of positive divisors of $x$ (including $1$ and $x$). Find $\tau\left( \tau\left( \dots \tau\left(2024^{2024^{2024}}\right) \right)\right)$, where there are $4202^{4202^{4202}}$ $\tau$'s.

Let's think step by step and output the final answer within \boxed{}.
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