
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 with diameter \(AC\) has a tangent \(BC\). The line segment \(AB\) intersects the circle at point \(D\). Another tangent to the circle is drawn through point \(D\), intersecting the line segment \(BC\) at point \(K\). In what ratio does point \(K\) divide the segment \(BC\)?

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