
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 $f(x)=\frac{ax}{e^x}$, the equation of the tangent line at $x=0$ is $y=x$.

(1) If for any $x \in (0,2)$, $f(x) < \frac{1}{k+2x-x^2}$ holds, find the range of values for $k$;

(2) If the function $g(x)=\ln f(x)-b$ has two zeros $x_1, x_2$, determine the sign of $g''\left(\frac{x_1+x_2}{2}\right)$ and explain the reason.

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