
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 common chord length of the two circles $x^{2}+y^{2}+4x-4y=0$ and $x^{2}+y^{2}+2x-12=0$ can be found by calculating the value of $\sqrt{(1^{2}+2^{2})^{2} - (4 - (-4) + 2 + 12)}$.

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