
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
A travel agency arranges a tour group to travel by air, with a package airfare of 18,000 yuan. The airfare for each person in the tour group is settled with the travel agency as follows: If the number of people in the tour group does not exceed 35, each air ticket is 800 yuan; if the number of people in the tour group exceeds 35, a discount will be given. For each additional person, the airfare for each person will be reduced by 10 yuan. However, the number of people in the tour group should not exceed 60. Let x be the number of people in the tour group, y be the airfare per person, and Q be the profit of the travel agency.

1. Write the functional relationship between the airfare per person y (in yuan) and the number of people in the tour group x.
2. For what value of x can the travel agency obtain the maximum profit? Find the maximum profit.

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