
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
The approximate relationship between the total demand $f(x)$ (in tens of thousands of units) for a certain product in a certain region during the first few months starting from next year and the number of months $x$ is given by $f(x)=\frac{1}{150}x(x+1)(35-2x) (x\in N, x\leqslant 12)$.
(1) Write the functional relationship $g(x)$ (in tens of thousands of units) between the demand in the $x$-th month and the number of months $x$;
(2) Find the month number $x$ with the maximum demand and calculate the total demand for this $x$ months.

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