
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
Sunshine Rose Grape in Liangshan Prefecture, Sichuan Province is a very popular fruit. Its delicious taste and unique aroma have earned it a high reputation among consumers, making it an important industry for local farmers to increase their income. A research team found that the yield $s$ (unit: hundred kilograms) per acre of Sunshine Rose Grape is related to the fertilizer cost $x$ (unit: hundred yuan) as follows: $s=\frac{16}{5}-\frac{4}{x+1}$, and the fertilizer cost per acre does not exceed 500 yuan. In addition, an additional cost of 3x hundred yuan is required per acre for other expenses (such as labor costs for fertilization). It is known that the market price of this grape is 25 yuan per kilogram (equivalent to 25 hundred yuan per hundred kilograms), and the market demand always exceeds supply. Let the profit per acre obtained from planting this grape be denoted as $P(x)$.
1. Find the analytical expression of the profit function $P(x)$ per acre.
2. For what fertilizer cost per acre does planting this grape variety yield the maximum profit? What is the maximum profit?

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