
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
Sets \(A, B\), and \(C\) satisfy \(|A| = 92\), \(|B| = 35\), \(|C| = 63\), \(|A \cap B| = 16\), \(|A \cap C| = 51\), and \(|B \cap C| = 19\). Compute the number of possible values of \(|A \cap B \cap C|\).

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