
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|.
(1) When a = 1 and b = 1, find the solution set for the inequality f(x) ≤ 4.
(2) If a > 0 and b > 0, and the minimum value of f(x) is 2, find the minimum value of $\frac{1}{a} + \frac{2}{b}$.

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