
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 the geometric sequence \\(\{a_n\}\) satisfy that the common ratio \\(q \in \mathbb{N}^*\) and \\(a_n \in \mathbb{N}^*\), and the product of any two terms in \\(\{a_n\}\) is also a term in the sequence. If \\(a_1 = 2^{81}\), then the set of all possible values of \\(q\) is \_\_\_\_\_\_.

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