
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 store counter sells a product, with each unit costing 10 yuan to produce, and each unit also incurs a management fee of a yuan (3≤a≤7) paid to the store. It is estimated that when the selling price per unit is x yuan (20≤x≤25), the daily sales volume will be (x−30)<sup>2</sup> units. (Ⅰ) Find the function relationship between the daily profit $f(x)$ (in yuan) of the counter and the selling price per unit $x$;  
(Ⅱ) At what selling price per unit will the daily profit $f(x)$ of the counter be maximized, and find the maximum value of $f(x)$, denoted as $g(a)$.

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