
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
Bob sends a secret message to Alice using her RSA public key  $n = 400000001.$  Eve wants to listen in on their conversation. But to do this, she needs Alice's private key, which is the factorization of  $n.$  Eve knows that  $n = pq,$  a product of two prime factors. Find  $p$  and  $q.$ 

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