
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
Determine the value(s) of $y$ for which the pair of equations $x^2 + y^2 - 9 = 0$ and $x^2 + 2y - 7 = 0$ may have real common solutions.
**A)** $1 + \sqrt{3}$ and $1 - \sqrt{3}$ only  
**B)** $1 + \sqrt{3}$ only  
**C)** $1 - \sqrt{3}$ only  
**D)** $0$  
**E)** No real $y$

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