
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 integral  $k>1$ , we let  $p(k)$  be its smallest prime divisor. Given an integer  $a_1>2$ , we define an infinite sequence  $a_n$  by  $a_{n+1}=a_n^n-1$  for each  $n\geq 1$ . For which values of  $a_1$  is the sequence  $p(a_n)$  bounded?

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