
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 company recently promoted a product, and the sales volume $P$ (in ten thousand units) was found to be related to the promotional cost $x$ (in ten thousand yuan) by the function $P=3-\frac{2}{x+1}$ (where $0 \leqslant x \leqslant a$, $a$ is a positive constant). The production cost for this product is $10 + 2P$ (in ten thousand yuan, excluding promotional costs), and the selling price is set at $(4 + \frac{30}{P})$ yuan/unit. Assume that the production volume equals the sales volume.
(I) Express the profit $y$ (in ten thousand yuan) as a function of the promotional cost $x$.
(II) Determine the promotional cost $x$ that maximizes the profit $y$.

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