
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
Let $y=f(x)$ be defined on $\mathbb{R}$. For a given positive number $K$, define $f_k(x) = \begin{cases} f(x), & \text{if } f(x) \leq K \\ K, & \text{if } f(x) > K \end{cases}$. Let the function $f(x) = 2 - x - \frac{1}{e^x}$. If for any $x \in \mathbb{R}$, it always holds that $f_k(x) = f(x)$, determine the value of $K$.

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