
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 nonempty set \( S \) is called well-filled if for every \( m \in S \), there are fewer than \(\frac{1}{2} m\) elements of \( S \) which are less than \( m \). Determine the number of well-filled subsets of \(\{1,2, \ldots, 42\}\).

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