
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 perfect power is an integer \( n \) that can be represented as \( a^{k} \) for some positive integers \( a \geq 1 \) and \( k \geq 2 \). Find the sum of all prime numbers \(0 < p < 50\) such that \( p \) is 1 less than a perfect power.

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