
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 four prime numbers \( p_1, p_2, p_3, p_4 \) satisfying 
\[ 
\begin{array}{l}
p_1 < p_2 < p_3 < p_4, \\
p_1 p_2 + p_2 p_3 + p_3 p_4 + p_4 p_1 = 882,
\end{array}
\]
find the values of these four prime numbers.

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