
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 that the function $y=f(x)$ is defined within $(-\infty, +\infty)$, a new function $f\_K(x)$ is defined for a given positive number $K$ as follows: $f\_K(x) = \begin{cases} f(x), & f(x) \leqslant K \\ K, & f(x) > K \end{cases}.$ Consider the function $f(x) = 2^{-|x|}.$ When $K = \frac{1}{2}$, identify the interval(s) where the function $f\_K(x)$ is monotonically increasing.

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