
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 graphs of the functions \( x^{2}+y^{2}=4+12 x+6 y \) and \( x^{2}+y^{2}=k+4 x+12 y \) intersect each other for different values of \( k \) that satisfy \( a \leqslant k \leqslant b \). Find the value of \( b-a \).

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