
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,n$  be positive integers, and let  $ F$  be a family of  $ m$ -element subsets of  $ \{1,2,...,n\}$  satisfying  $ A\cap B \not \equal{} \emptyset$  for all  $ A,B\in F$ . Determine the maximum possible number of elements in  $ F$ .

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