
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 $f(x)=\frac{{4}^{x}}{{4}^{x}+2}$, where $y=\left[x\right]$ is the Gaussian function representing the largest integer not exceeding the real number $x$, find the relationship between sets $A=\{-2,-1,0,1\}$ and $B=\{y|y=[f(x)-\frac{1}{2}]+[f(1-x)-\frac{1}{2}],x∈R\}$.

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