
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) = |2x - 1| + |x - 1|.
(I) Find the solution set for the inequality f(x) ≤ 4.
(II) Let m be the minimum value of the function f(x). When a, b, c ∈ ℝ^+, and a + b + c = m, find the maximum value of $\sqrt{2a + 1} + \sqrt{2b + 1} + \sqrt{2c + 1}$.

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