
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 $f(x) = |2x-1| + |5x-1|$,  
(1) Find the solution set for $f(x) > x + 1$;  
(2) If $m = 2 - n$, for all $m, n \in (0, +\infty)$, it always holds that $\frac{1}{m} + \frac{4}{n} \geq f(x)$, find the range of the real number $x$.

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