
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 + m| + |2x - n|, where m, n ∈ (0, +∞).
(I) Find the minimum value of 2m + n if f(x) ≥ 1 always holds true.
(II) If m = 2 and n = 3, find the solution set for the inequality f(x) > 5.

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