
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
Given \( n = p \cdot q \cdot r \cdot s \), where \( p, q, r, s \) are distinct primes such that:

1. \( s = p + r \)
2. \( p(p + q + r + s) = r(s - q) \)
3. \( qs = 1 + qr + s \)

Find \( n \).

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