
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 prime number  $p$  is mundane if there exist positive integers  $a$  and  $b$  less than  $\tfrac{p}{2}$  such that  $\tfrac{ab-1}{p}$  is a positive integer. Find, with proof, all prime numbers that are not mundane.

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