
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
The so-called "Plato's rule." If one leg of a right triangle is an even number $2p$, then the other leg will be $p^2 - 1$, and the hypotenuse will be $p^2 + 1$. Verify and calculate the sides of the triangles for $p = 2, 3, 4, 5$.

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