
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
There are 11 sets \( M_1, M_2, \cdots, M_{11} \), each with 5 elements, and every pair of sets has a non-empty intersection. Find the minimum possible value of the maximum number of sets that share a common element.


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