
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Consider a polynomial product of the form
\[
(1 - z)^{a_1} (1 - z^2)^{a_2} (1 - z^3)^{a_3} (1 - z^4)^{a_4} \dotsm (1 - z^{10})^{a_{10}},
\]
where the $a_k$ are positive integers. This polynomial, when expanded and terms with powers of $z$ greater than 10 are discarded, simplifies to $1 - 3z$. Determine $a_{10}$.

Present the answer in LaTex format: \boxed{Your answer}
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