
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 equations $x^2 + y^2 - 9 = 0$ and $x^2 - 2y + 6 = 0$ may have a real common solution.
A) -5 only
B) 3 only
C) -5 and 3
D) No $y$
E) All $y$

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