
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 store is test-selling a type of clothing with a cost of 60 yuan per item. It is stipulated that during the test sale period, the selling price per item must not be lower than the cost price, and the profit must not exceed 40%. It was found during the test sale that the sales volume $y$ (in pieces) and the selling price $x$ (in yuan) follow a linear function $y=kx+b$, and when $x=80$, $y=40$; when $x=70$, $y=50$.
(1) Find the expression of the linear function $y=kx+b$;
(2) If the profit of the store is $W$ yuan, write the relationship between the profit $W$ and the selling price $x$; at what selling price will the store obtain the maximum profit, and what is the maximum profit in yuan?

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