
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) Solve the inequality $f(x) < 4$;  
(2) If the function $g(x) = f(x) + f(x-1)$ has a minimum value of $a$, and $m+n=a$ ($m>0$, $n>0$), find the range of values for $\frac{2}{m} + \frac{1}{n}$.

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