
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 tea specialty store sells a certain brand of tea, with a cost price of $80$ yuan per kilogram and a selling price not less than $120$ yuan per kilogram and not more than $180$ yuan per kilogram. After a period of time, the following data is obtained:

| Selling Price $x$ (yuan/kg) | $120$ | $130$ | $\ldots$ | $180$ |
|-----------------------------|-------|-------|----------|-------|
| Daily Sales $y$ (kg)        | $100$ | $95$  | $\ldots$ | $70$  |

It is assumed that the relationship between $y$ and $x$ is a type of function we have learned.

(1) Write down the functional relationship between $y$ and $x$ directly, and indicate the range of values for the independent variable $x$.

(2) At what selling price is the profit maximized? What is the maximum profit?

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