
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
At a conference with $30$ businessmen, fifteen businessmen drank coffee, twelve businessmen drank tea, and eight businessmen drank juice. Six businessmen drank both coffee and tea, four drank both coffee and juice, and two drank both tea and juice. One businessman drank all three beverages. How many businessmen drank neither coffee, tea, nor juice?

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