
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| + |x - 3| (m > 0).
(I) If m = 1, find the solution set of the inequality f(x) ≥ 4.
(II) If the minimum value of f(x) is 3, and $\frac{1}{p} + \frac{1}{2q} = m$ (p > 0, q > 0), find the minimum value of pq.

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