
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 shopping mall estimated that in 2018, the demand $f(x)$ for a certain product in the $x$-th month is approximately related to $x$ as follows: $f(x) = -3x^2 + 40x$ (where $x \in \mathbb{N}^*$, $1 \leq x \leq 12$). The monthly purchase unit price $q(x)$ (in Yuan) for the product is approximately $q(x) = 150 + 2x$ (where $x \in \mathbb{N}^*$, $1 \leq x \leq 12$), and the selling price for each item is 185 Yuan. Assuming other costs are negligible and the market demand can be met each month, which month of 2018 will the shopping mall have the highest monthly profit for this product, and how much is this maximum monthly profit?

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