
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
Complex numbers \( p, q, r \) form a right triangle in the complex plane where \( pq \) is the hypotenuse with length 24 and \( pr \), \( qr \) are the legs with lengths 10 and \( \sqrt{476} \) respectively. If \( \left| p + q + r \right| = 40 \), find \( \left| pq + pr + qr \right| \).

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