
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
From a point outside a circle, two tangent lines and a secant line are drawn such that the points of tangency and the points where the secant intersects the circle are the vertices of a certain trapezoid. Find the ratio of the bases of the trapezoid, given that the angle between the tangents is $60^{\circ}$.

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