
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 center of a circle with radius 6, which is tangent to the sides $AB$, $BC$, and $CD$ of an isosceles trapezoid $ABCD$, lies on its larger base $AD$. The base $BC$ is equal to 4. Find the distance between the points where the circle touches the lateral sides $AB$ and $CD$ of this trapezoid.

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