
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 $y=f(x)=2^{-|x|}$ and the function $f_{K}(x)$ defined as $f(x)$ for $f(x) \leqslant K$ and $K$ for $f(x) > K$, find the interval of monotonic increase for $f_{K}(x)$ when $K=\frac{1}{2}$.

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