
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 $f(x) = x^2 + kx + 5$, $g(x) = 4x$, and let the value range of the function $y = 4^x - 2^{x+1} + 2$ be $D$ when $x \leq 1$. If for $x \in D$, it always holds that $f(x) \leq g(x)$, find the range of the real number $k$.

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