
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 shopping mall's sales experience of a certain product shows that the daily sales volume $y$ (unit: kg) of the product is related to the selling price $x$ (unit: yuan/kg) by the equation $y=\dfrac{a}{x-5}+10\left(x-8\right)^{2}$, where $5 \lt x \lt 8$, and $a$ is a constant. It is known that when the selling price is $7$ yuan/kg, the product can be sold at a rate of $11$ kg per day.

(I) Find the value of $a$.

(II) If the cost of the product is $5$ yuan/kg, determine the value of the selling price $x$ that maximizes the profit obtained by the shopping mall from selling the product daily.

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