
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 department store's experience in selling a type of commodity shows that the daily sales volume $y$ (in kilograms) is related to the selling price $x$ (in yuan per kilogram) by the equation: $y = \frac{a}{x-3} + 10(x-6)^2$, where $3 < x < 6$ and $a$ is a constant. When the selling price is 5 yuan per kilogram, the store can sell 11 kilograms of the product per day.
(1) Find the value of $a$;
(2) If the cost of the product is 3 yuan per kilogram, determine the selling price $x$ that maximizes the store's daily profit from selling the product, and find the maximum profit.

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