
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
Compute the prime factorization of  $1007021035035021007001$ .  (You should write your answer in the form  $p_1^{e_1}p_2^{e_2}\ldots p_k^{e_k}$  where  $p_1,\ldots,p_k$  are distinct prime numbers and  $e_1,\ldots,e_k$  are positive integers.)

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