
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 set  $X$  of positive integers is said to be *iberic* if  $X$  is a subset of  $\{2, 3, \dots, 2018\}$ , and whenever  $m, n$  are both in  $X$ ,  $\gcd(m, n)$  is also in  $X$ . An iberic set is said to be *olympic* if it is not properly contained in any other iberic set. Find all olympic iberic sets that contain the number  $33$ .

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