
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 prime numbers  $p_1,…,p_n$  (not necessarily different) such that :  $$  \prod_{i=1}^n p_i=10 \sum_{i=1}^n p_i $$  

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