
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}
user