
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 triples  $(p, q, r)$  of prime numbers for which  $4q - 1$  is a prime number and   $$ \frac{p + q}{p + r} = r - p $$  holds.

*(Walther Janous)*

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