
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 offers a group travel package during the summer holidays with the following conditions: for a group of 100 people, the charge is 1000 yuan per person. For each additional person beyond 100 in the group, the average charge per person decreases by 5 yuan, but the group size cannot exceed 180 people. Let the number of people in the group be $x$, and let the total charge by the travel agency be $y$.
(1) Establish the functional relationship between the travel agency's charge $y$ and the group size $x$;
(2) How should the group be organized to maximize the travel agency's charge?

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