
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 \( T \) be the set of all positive divisors of \( 20044^{100} \). The subset \( S \) of \( T \) has the property that no element in \( S \) is an integer multiple of any other element in \( S \). Find the maximum possible number of elements in \( S \).

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