
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 the function $y=f(x)$ have a domain of $(0,+\infty)$. For a given positive number $K$, define $f_K(x)=\begin{cases} K, & f(x)\leqslant K \\ f(x), & f(x) > K \end{cases}$. 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