
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
If $A$, $B$, and $C$ are sets where $|A| = 3$, $|B| = 3$, and the sum of subsets of $A$, $B$, and $C$ equals the number of subsets of their union, $n(A)+n(B)+n(C)=n(A\cup B\cup C)$, determine the minimum possible value of $|A\cap B\cap C|$.

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