
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
Two circles whose radii are in the ratio \( 9-4\sqrt{3} \) touch each other internally. Two chords of the larger circle, which are equal in length and tangent to the smaller circle, are drawn. One of these chords is perpendicular to the segment connecting the centers of the circles, and the other is not. Find the angle between these chords.

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