
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
Find all positive integers \( k \leq 100 \) for which there exists an integer \( n \) such that \( 3 n^{6} + 26 n^{4} + 33 n^{2} + 1 \) is a multiple of \( k \).

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