
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 three sets such that:

-A$|-|A|=100$, $|B|=50$, and $|C|=48$,

-The number of elements belonging to exactly one of the three sets is twice the number of elements belonging to exactly two of the sets.

-The number of elements belonging to exactly one of the three sets is three times the number of elements belonging to all of the sets.

How many elements belong to all the sets?

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