
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 $2097$ are reversed, we obtain the number $7902$. Factorize $7902$ such that it equals $d \cdot e \cdot f$, where $d$, $e$, and $f$ are three distinct primes. How many other positive integers are the products of exactly three distinct primes $q_1$, $q_2$, and $q_3$ such that $q_1 + q_2 + q_3 = d+e+f$?

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