
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  $|A| = 92$ ,  $|B| = 35$ ,  $|C| = 63$ ,  $|A\cap B| = 16$ ,  $|A\cap C| = 51$ ,  $|B\cap C| = 19$ . Compute the number of possible values of $ |A \cap  B \cap C|$ .

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