
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 $f(x)=\frac{ax}{e^{x}+1}+be^{-x}$, the point $M(0,1)$ lies on the curve $y=f(x)$, and the tangent to the curve at the point $M$ is perpendicular to the line $2x-y=0$.

$(1)$ Find the values of $a$ and $b$.

$(2)$ If for all $x\neq 0$, we have $f(x) > \frac{x}{e^{x}-1}+ke^{-x}$, find the range of values for $k$.

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