
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
Given a cylindrical empty cup with a bottom diameter of $8cm$ and a height of $20cm$, the volume of the solution poured into the cup is a function of time $t$ ($t\geqslant 0$) and is represented as $V(t)=\pi t^{3}+2\pi t^{2}$ (unit: $ml$). Find the instantaneous rate of change of the height of the solution in the cup at $t=4s$.

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