
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 equation of the circle with the common chord of circle \\(C_{1}\\): \\(x^{2}+y^{2}-12x-2y-13=0\\) and circle \\(C_{2}\\): \\(x^{2}+y^{2}+12x+16y-25=0\\) as its diameter is ______________.

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