
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
Let $ABCD$ be an isosceles trapezoid, where $AB = 10, BC = 7 = DA,$ and $CD = 6$. Circles of radius 4 centered at $A$ and $B$, and circles of radius 3 centered at $C$ and $D$ are drawn. Find the radius $r$ of a circle contained within the trapezoid that is tangent to all four of these circles.

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