
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 diagonals of a cyclic quadrilateral \(ABCD\) intersect at point \(O\). Let \(K\) and \(L\) be the points of intersection of the circumcircle of triangle \(AOB\) with lines \(AD\) and \(BC\) respectively. Find the ratio \(OK : OL\), given that \(\angle BCA = \angle BDC\).

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