
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 branch sells a certain brand of product. Each product costs 3 yuan, and for each product, a management fee of 3 yuan must be paid to the head office. It is estimated that when the selling price per product is x yuan (9 ≤ x ≤ 11), the annual sales volume is (12 - x)^2 10,000 pieces.
(1) Find the function relationship between the annual profit y (in ten thousand yuan) of the branch and the selling price per product.
(2) At what selling price per product will the annual profit y of the branch be maximized, and what is the maximum value of y?

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