
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 $f(x) = 45|2x - 1|$.
(1) Find the solution set of the inequality $f(x) + |x + 1| < 2$.
(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 minimum value of $\frac{4}{m} + \frac{1}{n}$.

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