
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 \( X = \{1, 2, 3, 4, 5, 6, 7\} \). How many 7-tuples \((X_1, X_2, X_3, X_4, X_5, X_6, X_7)\) are there such that each \(X_i\) is a different subset of \(X\) with three elements and the union of the \(X_i\) is \(X\)?

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