
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 $f(x)=(x^2+ax-2a^2+3a)e^x$ where $x \in \mathbb{R}$ and $a \in \mathbb{R}$,

(I) When $a=0$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$;

(II) Discuss the monotonicity of the function $f(x)$;

(III) When $a=1$, given $\forall m, n \in [-3, 0]$, $|f(m)-f(n)|\leq M$ always holds, find the minimum value of M.

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