
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 with dimensions $AB = 8$, $BC = 7 = DA$, and $CD = 6$. Draw circles of radius 4 centered at $A$ and $B$, and circles of radius 3 centered at $C$ and $D$. A circle contained within the trapezoid is tangent to all four of these circles. Its radius is expressed in the form $\frac{-k + m \sqrt{n}}{p}$ where $k, m, n, p$ are positive integers. Find $k + m + n + p$.

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