
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 person sells a certain product and finds that the daily sales volume $y$ (in thousands of kilograms) and the sales price $x$ (in yuan per thousand kilograms) satisfy the relationship: $y=\begin{cases} \frac{150}{x-6}+a(x-9),6 < x < 9 \\ \frac{177}{x-6}-x,9\leqslant x\leqslant 15\end{cases}$, where $a$ is a constant.

It is known that when the sales price is 8 yuan per thousand kilograms, the daily sales volume is 80 thousand kilograms.

(I) Find the value of $a$;

(II) If the cost of the product is 6 yuan per thousand kilograms, find the value of the sales price $x$ that maximizes the daily profit from selling the product.

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