
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 $f(x)=me^{x}-x-1$, where $e$ is the base of the natural logarithm.
(1) If the curve $y=f(x)$ passes through the point $P(0,1)$, find the equation of the tangent line to the curve $y=f(x)$ at the point $P(0,1)$.
(2) If $f(x)$ has two zero points $x_{1}$ and $x_{2}$ with $x_{1} < x_{2}$, find the range of values of $y=(e^{x_{2}}-e^{x_{1}})( \frac {1}{e^{x_{2}}+e^{x_{1}}}-m)$.
(3) If $f(x) > 0$ always holds, compare the sizes of $e^{m-1}$ and $m^{e-1}$, and explain the reason.

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