
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 $f(x)=|2x-1|$.
(1) Find the solution set for the inequality $f(x) < 4$.
(2) 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 range of values for $\frac{m^{2}+2}{m}+ \frac{n^{2}+1}{n}$.

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