
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
Selected Exercise $(4-5)$: Inequality Lecture.

Given the function $f(x)=|2x-1|$.

(I) Find the solution set of the inequality $f(x)+|x+1| < 2$.

(II) If the minimum value of the function $g(x)=f(x)+f(x-1)$ is $a$, and $m+n=a (m > 0, n > 0)$, find the minimum value of $\frac{4}{m}+\frac{1}{n}$.

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