
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 $a\in\mathbb{R}$, the function $f(x)=-\frac{1}{3}x^3+\frac{1}{2}ax^2+2ax$ where $x\in\mathbb{R}$.
(1) When $a=1$, find the interval where the function $f(x)$ is monotonically increasing;
(2) If the function $f(x)$ is monotonically decreasing on $\mathbb{R}$, find the range of values for $a$.

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