
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 following pair of equations $x^2+y^2-16=0$ and $x^2-3y-12=0$ may have a real common solution.
**A)** $-4$ only  
**B)** $1$ only  
**C)** $-4$ and $1$  
**D)** No $y$  
**E)** All $y$

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