
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 $35$ businessmen, eighteen businessmen drank coffee, and fifteen businessmen drank tea. Seven businessmen drank both coffee and tea. Additionally, six businessmen drank juice, with three of them drinking both juice and tea but not coffee. How many businessmen drank neither coffee, tea, nor juice?

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