
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 $f(x) = |x-4|$,  
(Ⅰ) If $f(x) \leq 2$, find the range of $x$;  
(Ⅱ) Under the condition of (Ⅰ), find the maximum value of $g(x) = 2\sqrt{|x-2|} + \sqrt{|x-6|}$.

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