
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 that circle \(O_{1}: x^{2} + y^{2} = 2\) and circle \(O_{2}: (x-3)^{2} + y^{2} = 5\) have a common point \(A\) in the first quadrant. A line passing through point \(A\) intersects the circles \(O_{1}\) and \(O_{2}\) at points \(C\) and \(D\) respectively (other than point \(A\)), and \(\overrightarrow{AC} = 2 \overrightarrow{AD}\). Find the slope of line \(CD\).

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