
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
There are several different positive integers written on the blackboard, and the sum of any two different numbers should be should be a prime power. At this time, find the maximum possible number of integers written on the blackboard. A prime power is an integer expressed in the form  $p^n$  using a prime number  $p$  and a non-negative integer number  $n$ .

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