
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
A natural number is called a *prime power* if that number can be expressed as  $p^n$  for some prime  $p$  and natural number  $n$ . 
Determine the largest possible  $n$  such that there exists a sequence of prime powers  $a_1, a_2, \dots, a_n$  such that  $a_i = a_{i - 1} + a_{i - 2}$  for all  $3 \le i \le n$ . 

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