
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
Given two circles $\odot C_1: x^2 + y^2 + D_1x + E_1y - 3 = 0$ and $\odot C_2: x^2 + y^2 + D_2x + E_2y - 3 = 0$ both passing through the point A $(2, -1)$, find the equation of the line that simultaneously passes through the points $(D_1, E_1)$ and $(D_2, E_2)$.

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