
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 \(X\) be a set with 56 elements. Find the smallest positive integer \(n\) such that for any 15 subsets of \(X\), if the union of any seven of these subsets contains at least \(n\) elements, then there must exist three of these 15 subsets whose intersection is non-empty.

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