
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 $$f(x)=|x+ \frac {t}{2}|+ \frac {8-t^{2}}{4}$$ where $x \in \mathbb{R}$, if the function $F(x)=f[f(x)]$ and $y=f(x)$ have the same range for $x \in \mathbb{R}$, the range of real number $t$ is \_\_\_\_\_\_.

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