
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
Given  $a_0 > 1$ , the sequence  $a_0, a_1, a_2, ...$  is such that for all  $k > 0$ ,  $a_k$  is the smallest integer greater than  $a_{k-1}$  which is relatively prime to all the earlier terms in the sequence.
Find all  $a_0$  for which all terms of the sequence are primes or prime powers.

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