
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 the set $A=\{x|f(x)=\sqrt{2^x-1}\}$, and $B=\{y|y=\log_2(2^x+2)\}$. Find the intersection of set $A$ and the complement of set $B$ in the set of real numbers $\mathbb{R}$.

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