
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 $f(x)=x-e^{x}$ (where $e$ is the base of the natural logarithm) and $g(x)=mx+1$ (where $m\in\mathbb{R}$), if for any $x_{1}\in\left[-1,2\right]$, there always exists an $x_{0}\in\left[-1,1\right]$ such that $g(x_{0})=f(x_{1})$ holds true, then the range of values for the real number $m$ is (   ).

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