
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
The value(s) of $y$ for which the following pair of equations $x^2+y^2-16=0\text{ and }x^2-3y-12=0$ may have real common solutions are:
A) -4 only
B) 1 only
C) -4 and 1
D) No real values of y

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