
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
Find the value(s) of $y$ for which the following pair of equations $x^2 + y^2 - 4 = 0$ and $x^2 - 4y + 8 = 0$ may have a real common solution.
A) -6
B) 0
C) 2
D) -6, 2

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