
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
For any integer \( n (n \geqslant 4) \), consider the set \(\{1, 2, \cdots, n\}\) with \( m \) subsets \( A_{1}, A_{2}, \cdots, A_{m} \), where \( A_{1} \) has one element, \( A_{2} \) has two elements, ..., \( A_{m} \) has \( m \) elements, and no subset is contained within another subset. Find the maximum value of \( m \).

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