
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 product costs $6$ per unit, sells for $x$ per unit $(x > 6)$, and has an annual sales volume of $u$ ten thousand units. It is known that $\frac{585}{8} - u$ is directly proportional to $(x - \frac{21}{4})^2$, and when the selling price is $10$ dollars, the annual sales volume is $28$ ten thousand units.

(1) Find the relationship between the annual sales profit $y$ and the selling price $x$.
(2) Find the selling price that maximizes the annual profit and determine the maximum annual profit.

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