
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 sells a product at a cost of $10 per item, and each item incurs a management fee of $a$ $(3 \leqslant a \leqslant 7)$ to the store. It is estimated that when the selling price per item is $x$ dollars $(20 \leqslant x \leqslant 25)$, the daily sales volume will be $(x-30)^2$ items.  
(Ⅰ) Find the function relationship $f(x)$ (in dollars) between the daily profit of the counter and the selling price per item $x$;  
(Ⅱ) What should be the selling price per item to maximize the daily profit $f(x)$ of the counter, 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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