
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
A trapezoid \(ABCD\) is inscribed in a circle, with bases \(AB = 1\) and \(DC = 2\). Let \(F\) denote the intersection point of the diagonals of this trapezoid. Find the ratio of the sum of the areas of triangles \(ABF\) and \(CDF\) to the sum of the areas of triangles \(AFD\) and \(BCF\).

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