
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 2:3, touch each other internally. A line is drawn through the center of the smaller circle, perpendicular to the line connecting the centers. From the points where this line intersects the larger circle, tangents are drawn to the smaller circle. Find the angles between these tangents.

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