
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]


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To welcome the "Double Eleven" online shopping festival in 2014, a manufacturer plans to invest an appropriate amount of advertising fees to promote the products sold online. According to the survey, the sales volume $p$ (in ten thousand units) of the promoted product during "Double Eleven" and the promotional cost $x$ (in million yuan) satisfy the equation: $p=3-\frac{2}{x+1}$ (where $0 \leq x \leq a$, $a$ is a positive constant). It is known that the cost of producing this product requires an investment of $10+2p$ million yuan (excluding promotional costs), and the selling price of the product is set at $(4+\frac{20}{p})$ yuan/unit. Assuming that the manufacturer's production capacity can fully meet the market's sales demand:

(I) Express the profit $y$ (in million yuan) of this product as a function of the promotional cost $x$ (in million yuan);

(II) When will the manufacturer's profit be the highest if the promotional cost is invested? And find the maximum profit value.

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