
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 $f(x)=me^{x}-x-2$ where $e$ is the base of the natural logarithm,
$(1)$ If $f(x) > 0$ always holds on $\mathbb{R}$, find the range of values for $m$;
$(2)$ If $f(x)$ has two zeros $x_{1}$ and $x_{2}$, with $x_{1} < x_{2}$, find the range of values for $y=(e^{x_{2}}-e^{x_{1}})\left( \frac {1}{e^{x_{2}}+e^{x_{1}}}-m\right)$.

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