
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 possible value(s) of \(y\) for which the equations \(x^2 + y^2 - 4 = 0\) and \(x^2 - 4y + 8 = 0\) could have a common real solution.
A) 0
B) 2
C) 4
D) No \(y\)
E) All \(y\)

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