
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 $f(x)=ax^{3}-\frac{1}{2}x^{2}$ $(a > 0)$, $x\in[0,+\infty)$.
(1) If $a=1$, find the maximum and minimum values of the function $f(x)$ on $[0,1]$.
(2) If the decreasing interval of the function $y=f'(x)$ is $A$, explore the monotonicity of the function $y=f(x)$ on the interval $A$.

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