
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 certain company can produce up to $10$ lithography machines of a certain type per month. The revenue function for producing $x$ machines ($x \geqslant 1$, $x \in \mathbb{N}^{*}$) is $R(x) = x^2 + \frac{16}{x^2} + 40$ (in units of thousands of RMB), and its cost function is $C(x) = 10x + \frac{40}{x}$ (in units of thousands of RMB). (Please pay attention to the domain in the following questions)
1. Find the minimum value of the revenue function $R(x)$;
2. Find the maximum value of the marginal function $MC(x)$ of the cost function $C(x)$;
3. Find the minimum value of the profit $z(x)$ for producing $x$ machines of this type of equipment.

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