
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 economics, the marginal function $Mf(x)$ of a function $f(x)$ is defined as $Mf(x) = f(x+1) - f(x)$. A clothing company can produce up to 100 pieces per day. The revenue function for producing $x$ ($x \geq 1$) pieces is $R(x) = 300x - 2x^2$ (in yuan), and its cost function is $C(x) = 50x + 300$ (in yuan), where profit equals the difference between revenue and cost.  
(1) Find the profit function $p(x)$ and its marginal profit function $Mp(x)$.  
(2) Find the maximum values of the profit function $p(x)$ and its marginal profit function $Mp(x)$, respectively.

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