
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 that f(log₂x) = x - $\frac{1}{x}$.
(1) Find f(x);
(2) If 8^x - 8^(-x) - 4^(x+1) - 4^(1-x) + 8 ≥ kf(x) holds true for x ∈ [1, ∞), find the range of k.

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