
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
Suppose  $X$  is a set with  $|X| = 56$ . Find the minimum value of  $n$ , so that for any 15 subsets of  $X$ , if the cardinality of the union of any 7 of them is greater or equal to  $n$ , then there exists 3 of them whose intersection is nonempty.

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