
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 the acute-angled triangle $ABC$, the angle $\angle BAC = 60^\circ$. A circle constructed with $BC$ as the diameter intersects side $AB$ at point $D$ and side $AC$ at point $E$. Determine the ratio of the area of quadrilateral $BDEC$ to the area of triangle $ABC$.

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