
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
A positive integer  $n$  is called *pretty* if there exists two divisors  $d_1,d_2$  of  $n$   $(1\leq d_1,d_2\leq n)$  such that  $d_2-d_1=d$  for each divisor  $d$  of  $n$  (where  $1<d<n$ ).
Find the smallest pretty number larger than  $401$  that is a multiple of  $401$ .

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