
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 set $A=\{(x,y)|x+y=1\}$, and a mapping $f: A \rightarrow B$ such that under the action of $f$, the image of the point $(x,y)$ is $(2^x, 2^y)$. Then, the set $B$ is.

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