
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 $f(x)=-\frac{1}{3}x^{3}+2ax^{2}-3a^{2}x+a (a\in \mathbb{R})$.
(I) When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(3,f(3))$;
(II) Find the monotonic intervals and extreme values of the function $f(x)$;
(III) If $f(x) < a+1$ for any $x\in (3a, a)$, find the range of values of $a$.

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