
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 shopping mall sells a certain product. The daily sales volume $y$ (in kilograms) of this product is related to the sales price $x$ (in yuan per kilogram) by the equation $y = \frac{a}{x-4} + 100(8-x)$, where $4 < x < 8$ and $a$ is a constant. It is known that when the sales price is 6 yuan per kilogram, 220 kilograms of the product can be sold daily.
(1) Find the value of $a$;
(2) If the cost price of the product is 4 yuan per kilogram, determine the sales price $x$ that maximizes the daily profit from selling this product, and find the maximum profit.

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