
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
Three catering companies offer different pricing plans. The first company charges a basic fee of $\$120$ plus $\$18$ per person. The second company charges a basic fee of $\$220$ plus $\$13$ per person. The third company charges a basic fee of $\$150$ plus $\$15$ per person. Determine the least number of people for which the third company becomes the cheapest option.

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