
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
When the digits in the number $2017$ are reversed, we obtain the number $7102$. Factorize $7102$ into the product of three distinct primes $p$, $q$, and $r$. How many other positive integers are the products of exactly three distinct primes $p_1$, $p_2$, and $p_3$ such that $p_1 + p_2 + p_3 = p + q + r$?

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