
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
Determine all quadruples \(\left(p_{1}, p_{2}, p_{3}, p_{4}\right)\), where \(p_{1}, p_{2}, p_{3}, p_{4}\) are all prime numbers, and satisfy:
(1) \(p_{1}<p_{2}<p_{3}<p_{4}\);
(2) \(p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{4}+p_{4} p_{1}=882\).

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