
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 circle is inscribed in an angle with vertex \( A \), touching the sides of the angle at points \( B \) and \( C \). A line passing through \( A \) intersects the circle at points \( D \) and \( E \). The chord \( B X \) is parallel to the line \( D E \). In what ratio does the line \( X C \) divide the chord \( D E \)?

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