
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 be $f(x) = \left(ax^{2}-(4a+1)x+4a+3\right)e^{x}$.

(I) If the tangent line to the graph of $y=f(x)$ at point $(1,f(1))$ is parallel to the x-axis, find the value of $a$.

(II) If $f(x)$ has a local minimum at $x=2$, determine the range of values for $a$.

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