
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 the function $f(x)=2x^{3}+3ax^{2}+1 (x \in R)$.
(I) If $f(x)$ takes an extreme value at $x=1$, find the value of the real number $a$;
(II) Find the monotonic intervals of $f(x)$;
(III) Find the minimum value of the function $f(x)$ on the closed interval $[0,2]$.

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