
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
Sequence \(a_{1}, a_{2}, \cdots\) is defined as follows: \(a_{n}=2^{n}+3^{n}+6^{n}-1\), for \(n=1,2,3, \cdots\). Find all positive integers that are relatively prime to every term of this sequence.

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