
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 village plans to build an open cylindrical water tank (ignoring the thickness). Let the radius of the base of the tank be $r$ meters, the height be $h$ meters, and the volume be $V$ cubic meters. Assume that the construction cost is only related to the surface area, with the side area costing $100$ yuan/square meter and the base costing $160$ yuan/square meter. The total construction cost of the tank is $12000π$ yuan ($π$ is the circumference ratio).
(I) Express $V$ as a function of $r$, $V(r)$, and determine its domain;
(II) Discuss the monotonicity of the function $V(r)$, and determine the values of $r$ and $h$ when the volume of the tank is maximum.

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