
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 a function $f(x)$ defined on the domain $\mathbb{R}$ that satisfies $f(x+2)=2f(x)$, when $x \in [0, 2]$, $f(x) = \begin{cases} x^2 - x, & x \in [0, 1) \\ \frac{1}{10}(x - 2), & x \in [1, 2]. \end{cases}$ If $f(x) \geq t^2 - 2t - 4$ always holds true when $x \in [4, 6]$, find the range of the real number $t$.

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