
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
For positive integers \( n \), define
\[ a_{n} = 3^{n} + 6^{n} - 2^{n}. \]

Find, with proof, all primes that do not divide any of the numbers \( a_{1}, a_{2}, a_{3}, \ldots. \)

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