
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
Find all arrays \((p, q, r)\) that satisfy the following conditions:
1. \(p, q, r \in \mathbf{N}^{\cdot}\) and \(p \geq q \geq r\);
2. At least two of \(p, q, r\) are prime numbers;
3. \(\frac{(p+q+r)^{2}}{pqr}\) is a positive integer.

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