
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
If  $p$ ,  $q$ , and  $r$  are nonzero integers satisfying \[p^2+q^2 = r^2,\] compute the smallest possible value of  $(p+q+r)^2$ .

*Proposed by David Altizio*

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