
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 *interoceanic* if its prime factorization   $$ N=p_1^{x_1}p_2^{x_2}\cdots p_k^{x_k} $$  satisfies   $$ x_1+x_2+\dots +x_k=p_1+p_2+\cdots +p_k. $$  Find all interoceanic numbers less than 2020.

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