
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 $C_1$: $x^2 + y^2 + D_1x + E_1y + 3 = 0$ and $C_2$: $x^2 + y^2 + D_2x + E_2y + 3 = 0$ both pass through the point $A(1, 1)$, find the equation of the straight line passing through the points $(D_1, E_1)$ and $(D_2, E_2)$.

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