
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) = |x-2| - |x-1|.
(1) If positive numbers a and b satisfy a + 2b = f(-1), find the minimum value of $\frac{2}{a} + \frac{1}{b}$;
(2) Solve the inequality f(x) > $\frac{1}{2}$.

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