
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 $1234$ are reversed, we obtain the number $4321.$ Factorize $4321$ into a product of three distinct primes $p_1, p_2, p_3$ and find how many other positive integers are the products of exactly three distinct primes $q_1, q_2, q_3$ such that $q_1 + q_2 + q_3 = p_1 + p_2 + p_3$.

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