
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
Find the equation of the line on which the chord common to the circles $\rho=r$ and $\rho=-2r\sin\left(\theta+\frac{\pi}{4}\right)$ $(r > 0)$ lies.

A) $2\rho(\sin \theta+\cos \theta)=r$
B) $2\rho(\sin \theta+\cos \theta)=-r$
C) $\sqrt{2}\rho(\sin \theta+\cos \theta)=r$
D) $\sqrt{2}\rho(\sin \theta+\cos \theta)=-r$

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