
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|.

(I) Solve the inequality f(x) ≥ 7 - |x - 1| when a = 2.

(II) If the solution set of f(x) ≤ 1 is [0, 2] and m^2 + 2n^2 = a (m > 0, n > 0), find the maximum value of m + 4n.

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