
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 a function $y=f(x)$ with the domain $(0, +\infty)$, for a given positive number $K$, define $f_K(x) = \begin{cases} K, & \text{if } f(x) \leq K \\ f(x), & \text{if } f(x) > K \end{cases}$. When the function $f(x) = \frac{1}{x}$ and $K=1$, calculate $\int_{\frac{1}{4}}^{2} f_K(x) \, dx$.

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