
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 the interval $[0,1]$;
2. If the interval in which the derivative function $y=f'(x)$ decreases is denoted as $A$, investigate 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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