
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 shipbuilding company has a maximum annual shipbuilding capacity of 20 ships. The revenue function for building $x$ ships is $R(x) = 3700x + 45x^2 - 10x^3$ (in ten thousand yuan), and the cost function is $C(x) = 460x + 5000$ (in ten thousand yuan). In economics, the marginal function $Mf(x)$ of a function $f(x)$ is defined as: $Mf(x) = f(x+1) - f(x)$. Find:  
(1) The profit function $P(x)$ and the marginal profit function $MP(x)$;  
(2) How many ships should be built annually to maximize the company's annual profit?  
(3) The interval of decrease for the marginal profit function $MP(x)$, and explain the practical significance of the decrease in this context?

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