
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 functions $f(x)=x^{2}+ax+1$ and $g(x)=e^{x}$ ($a\in R$, $e$ is the constant $2.71828…$).

(1) If the line $y=kx$ is tangent to the graph of function $g(x)$, find the value of the real number $k$;

(2) If function $f(x)$ has a zero in the interval $(1,2)$, find the range of values for the real number $a$;

(3) Let $h(x)=f(x)\cdot g(x)$. Find the minimum value of function $h(x)$ in the interval $[-1,1]$.

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