
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
In recent days, a company has launched a promotional campaign for one of their products. It was calculated that the sales volume $P$ (in units of 10,000 pieces) and the promotional expenses $x$ (in units of 10,000 RMB) satisfy the function relationship: 
$$P = 3 - \frac{2}{x+1} \quad (0 \leq x \leq a, \text{ where } a \text{ is a positive constant}).$$

It is known that when the production quantity of this product is $P$ (in units of 10,000 pieces), an additional cost of $10 + 2P$ (in units of 10,000 RMB) (excluding promotional expenses) will be needed, and the sales price of the product is set as $(4 + \frac{30}{P})$ RMB/piece, assuming that the production volume is equal to the sales volume.

(Ⅰ) Express the profit $y$ (in units of 10,000 RMB) of this product as a function of the promotional expenses $x$ (in units of 10,000 RMB).

(Ⅱ) At what value of promotional expenses $x$ (in units of 10,000 RMB) does the product's profit $y$ (in units of 10,000 RMB) reach its maximum value?

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