
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
Define a function $f(x)$ with domain $\mathbb{R}$ that satisfies $f(x+2)=2f(x)$. When $x \in [-2,0]$, $f(x)=x^{2}+2x$. If for $x \in [2,4]$, $f(x) \geqslant 2\log_{2}^{(t+1)}$ always holds, then the range of the real number $t$ is \_\_\_\_\_\_.

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