
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
During the National Day period, a travel agency organized a group tour to a scenic area. If the number of people in the tour group is 30 or fewer, each person needs to pay a fee of 900 yuan; if the number of people in the tour group exceeds 30, a discount is given: for each additional person, the per capita cost decreases by 10 yuan, until it reaches the set number of 75 people. The travel agency needs to pay a total of 15,000 yuan for various expenses.  
(1) Write the function of the per capita cost $y$ in terms of the number of people $x$;  
(2) At what number of people in the tour group does the travel agency achieve the maximum profit?

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