
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
Let  $p_1,p_2,p_3,p_4$  be four distinct primes, and let  $1=d_1<d_2<\ldots<d_{16}=n$  be the divisors of  $n=p_1p_2p_3p_4$ . Determine all  $n<2001$  with the property that $d_9-d_8=22$ .

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