
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  $S = {1, 2, \cdots, 100}.$   $X$  is a subset of  $S$  such that no two distinct elements in  $X$  multiply to an element in  $X.$  Find the maximum number of elements of  $X$ . 

*2022 CCA Math Bonanza Individual Round #3*

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