
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
Given \( A_{1}, A_{2}, \cdots, A_{n} \) are \( n \) non-empty subsets of the set \( A=\{1,2,3, \cdots, 10\} \), if for any \( i, j \in \{1,2,3, \cdots, n\} \), we have \( A_{i} \cup A_{j} \neq A \), then the maximum value of \( n \) is \(\qquad\).

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