
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 $y=f(x), x \in \mathbb{R}$, for a given positive number $M$, define the function $f_{M}(x)=\begin{cases}f(x), & f(x) \leqslant M \\ M, & f(x) > M\end{cases}$. Let the function $f(x)=2-x-e^{-x}$. If for any $x \in \mathbb{R}$ it always holds that $f_{M}(x)=f(x)$, find the maximum value of $M$.

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