
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
Let set $A=\{(x,y) | x+y=1, x\in \mathbb{R}, y\in \mathbb{R}\}$. For any element $(x,y)$ in set $A$, there is a rule $f$ that maps $(x,y)$ to $(3^x, 3^y)$. Find the image set of $A$ under the rule $f$.

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