
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
In triangle \(ABC\), point \(D\) lies on side \(AC\), such that \(AD = 2DC\). Point \(E\) lies on side \(BC\). The area of triangle \(ABD\) is 3, and the area of triangle \(AED\) is 1. Segments \(AE\) and \(BD\) intersect at point \(O\). Find the ratio of the areas of triangles \(ABO\) and \(OED\).

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