
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
Let  $p$  be a prime number. A rational number  $x$ , with  $0 < x < 1$ , is written in lowest terms. The rational number obtained from  $x$  by adding  $p$  to both the numerator and the denominator differs from  $x$  by  $1/p^2$ . Determine all rational numbers  $x$  with this property.

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