
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 certain company distributes a type of green tea, with a cost of $50 per kilogram. A market survey found that the sales volume $w$ (in kilograms) varies with the selling price $x$ (in dollars per kilogram) during a period of time, with the specific relationship being $w=-2x+240$. Let the profit of selling this green tea during this period be $y$ (in dollars). Answer the following questions:<br/>$(1)$ Find the relationship between $y$ and $x$;<br/>$(2)$ For what value of $x$ is the value of $y$ maximized?

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