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

(1) If $f(x)$ has an extremum at $x=0$, determine the value of $a$, and find the equation of the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$;

(2) If $f(x)$ is a decreasing function on $[3,+\infty)$, find the range of values for $a$.

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