
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 11 sets \( M_{1}, M_{2}, \cdots, M_{11} \), each with exactly 5 elements, and for all \( i, j \) such that \( 1 \leq i < j \leq 11 \), \( M_{i} \cap M_{j} \neq \varnothing \), find the minimum possible value of the maximum number of sets that have a non-empty intersection.

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