
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 \(ABC\), a line is drawn from vertex \(A\) intersecting side \(BC\) at point \(D\), which is between points \(B\) and \(C\), such that \(\frac{CD}{BC} = \alpha\) where \(\alpha < \frac{1}{2}\). A point \(E\) is taken on side \(BC\) between points \(B\) and \(D\). A line through \(E\) parallel to side \(AC\) intersects side \(AB\) at point \(F\). Find the ratio of the areas of trapezoid \(ACEF\) and triangle \(ADC\) if it is known that \(CD = DE\).

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