
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 \( M = \{1, 2, \cdots, 10\} \), and \( A_1, A_2, \cdots, A_n \) be distinct non-empty subsets of \( M \). If \(i \neq j\), then \( A_i \cap A_j \) can have at most two elements. Find the maximum value of \( n \).

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