
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  $M_1, M_2, . . ., M_{11}$  be  $5-$ element sets such that  $M_i \cap M_j \neq {\O}$  for all  $i, j \in \{1, . . ., 11\}$ . Determine the minimum possible value of the greatest number of the given sets that have nonempty intersection.

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