
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
Let the function $f(x) = [ax^{2}-(3a+1)x+3a+2]e^{x}$.  
(I) If the slope of the tangent line to the curve $y=f(x)$ at the point $(2,f(2))$ is $0$, find $a$;  
(II) If $f(x)$ has a minimum value at $x=1$, find the range of values for $a$.

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