
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 of 56 elements. Determine the smallest positive integer \( n \) such that for any 15 subsets of \( X \), if the union of any 7 of these subsets has at least \( n \) elements, then there are at least 3 of these 15 subsets whose intersection is non-empty.

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