
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 chain store sells a certain product, with each item costing $4 and requiring a management fee of $a (where $1 \leq a \leq 3$) to be paid to the headquarters. The projected annual sales volume is $(10 - x)^2$ ten thousand units when the selling price per item is $x (where $7 \leq x \leq 9$).
(I) Derive the function $L(x)$ that represents the chain store's annual profit (in ten thousand dollars) in relation to the selling price $x$;
(II) Determine the selling price per item that maximizes the chain store's annual profit $L$, and find the maximum value of $L$.

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