
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
Suppose there are three caterers. The first charges a basic fee of $120 and $18 per person. The second charges a basic fee of $250 and $14 per person. A third caterer charges a flat rate of $20 per person with no basic fee. Determine the least number of people for which the third caterer becomes the cheapest option.

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