
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 prime number  $p$ . It is known that for each integer  $a$  such that  $1<a<p/2$  there exist integer  $b$  such that  $p/2<b<p$  and  $p|ab-1$ . Find all such  $p$ .

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