
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  $p$ ,  $q$ ,  $r$ , and  $s$  be 4 distinct primes such that  $p+q+r+s$  is prime, and the numbers  $p^2+qr$  and  $p^2+qs$  are both perfect squares. What is the value of  $p+q+r+s$ ?

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