
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  $\emph{well-filled}$  if for every  $m \in S$ , there are fewer than  $\frac 12 m$  elements of  $S$  which are less than  $m$ .
Determine the number of well-filled subsets of  $\left\{ 1,2,\dots,42 \right\}$ .

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