
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 natural numbers  $a>1$ , with the property that every prime divisor of  $a^6-1$  divides also at least one of the numbers  $a^3-1$ ,  $a^2-1$ .

*K. Dochev*

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