
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
The extension of the altitude \( BH \) of triangle \( ABC \) intersects the circle circumscribed around it at point \( D \) (points \( B \) and \( D \) lie on opposite sides of line \( AC \) ). The degree measures of arcs \( AD \) and \( CD \), not containing point \( B \), are \( 60^\circ \) and \( 90^\circ \) respectively. Determine the ratio in which segment \( BD \) is divided by side \( AC \).

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