
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
For a set S, let |S| represent the number of elements in S, and let n(S) represent the number of subsets of S, including the empty set and S itself. If sets A, B, and C satisfy n(A) + n(B) + n(C) = n(A ∪ B ∪ C) and |A| = |B| = 100, find the minimum possible value of |A ∩ B ∩ C|.

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