
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 $A$, $B$, and $C$ be sets with $|A| = 120$, $|B| = 120$, and $|C| = 130$. Determine the minimum possible value of $|A \cap B \cap C|$, given that $n(A) + n(B) + n(C) = n(A \cup B \cup C)$.

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