
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
One caterer charges a basic fee of \$50 plus \$18 per person. A second caterer charges a basic fee of \$180 plus \$15 per person, but offers a \$30 discount on the basic fee for groups of 30 or more people. What is the least number of people for which the second caterer is cheaper?

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