
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 + a| - |x - b| (a > 0, b > 0).
(I) Solve the inequality f(x) > 2 when a = 1 and b = 2.
(II) If the maximum value of function f(x) is 3, find the minimum value of $\frac{1}{a} + \frac{2}{b}$.

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