
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
An integer number  $m\geq 1$  is *mexica* if it's of the form  $n^{d(n)}$ , where  $n$  is a positive integer and  $d(n)$  is the number of positive integers which divide  $n$ . Find all mexica numbers less than  $2019$ .

Note. The divisors of  $n$  include  $1$  and  $n$ ; for example,  $d(12)=6$ , since  $1, 2, 3, 4, 6, 12$  are all the positive divisors of  $12$ .

*Proposed by Cuauhtémoc Gómez*

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