
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) < |x - 2| + 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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