
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

Let \(a_{1}, a_{2}, \cdots, a_{17}\) be a permutation of \(1, 2, \cdots, 17\), satisfying
$$
\left(a_{1}-a_{2}\right)\left(a_{2}-a_{3}\right) \cdots\left(a_{16}-a_{17}\right)\left(a_{17}-a_{1}\right) = 2^{n}.
$$

Find the maximum value of the positive integer \(n\).

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