
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 research team found that the yield of a peach tree $w$ (unit: 100 kg) and the cost of fertilizer (unit: 100 yuan) satisfy the following relationship: $w=4- \dfrac{3}{x+1}$, and the cost of fertilizer does not exceed 500 yuan. In addition, other costs (such as labor costs for fertilization) of $2x$ hundred yuan are also required. It is known that the market selling price of this kind of peach is 16 yuan/kg (i.e., 1600 yuan/100 kg), and the market demand always exceeds supply. Let the profit obtained from this peach tree be $L(x)$ (unit: 100 yuan).

(Ⅰ) Find the function relationship of the profit function $L(x)$, and write down its domain;

(Ⅱ) How much should the cost of fertilizer be to maximize the profit from this peach tree? What is the maximum profit?

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