
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 - m|.
(1) If the solution set of the inequality f(x) ≤ 6 is {x | -2 ≤ x ≤ 4}, find the value of the real number m.
(2) Under the condition of (1), if the inequality f(x) + f($$\frac{1}{2}$$x + 3) $$≤ \frac{8}{a} + \frac{2}{b}$$ holds true for all positive real numbers a and b that satisfy a + b = 2, find the range of x.

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