
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 produces 20 ships per year. It is known that the revenue function of building $x$ ships is $R(x) = 3700x + 45x^2 - 10x^3$ (unit: ten thousand yuan), and the cost function is $C(x) = 460x + 5000$ (unit: ten thousand yuan). In economics, the marginal function $Mf(x)$ of a function $f(x)$ is defined as $Mf(x) = f(x+1) - f(x)$.
(1) Find the profit function $P(x)$ and the marginal profit function $MP(x)$; (Hint: profit = revenue - cost)
(2) How many ships should the company plan to build per year to maximize its annual profit?
(3) Find the decreasing interval of the marginal profit function $MP(x)$ and explain what the decreasing nature of the function means in this context.

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