
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
A polynomial product of the form
\[
(1 - z)^{a_1} (1 - z^2)^{a_2} (1 - z^3)^{a_3} \dotsm (1 - z^{16})^{a_{16}},
\]
where \( a_k \) are positive integers, has the property that if we multiply it out and discard all terms involving \( z \) to a power larger than 16, what remains is just \( 1 - z. \) Determine \( a_{16} \).

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