
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
**8.** Find all integers  $a>1$  for which the least (integer) solution  $n$  of the congruence  $a^{n} \equiv 1 \pmod{p}$  differs from 6 (p is any prime number). **(N. 9)**

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