
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 this question, the full score is 12 points)  
In economics, the marginal function $Mf(x)$ of a function $f(x)$ is defined as $Mf(x) = f(x + 1) - f(x)$. The income of a company producing $x$ units of a certain product per month is $R(x)$ yuan, and the cost is $C(x)$ yuan, where $R(x) = 3000x - 20x^2$, $C(x) = 500x + 4000$ ($x \in \mathbb{N}^*$). It is known that the company produces no more than 100 units of the product per month.  
(1) Find the profit function $P(x)$ and its marginal profit function $MP(x)$.  
(2) Find the difference between the maximum value of the profit function and the maximum value of the marginal profit function.

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