
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 bases $AB = 80$ and $CD = 17$. Suppose $AD = BC = x$, and a circle with center on line segment $\overline{AB}$ is tangent to $\overline{AD}$ and $\overline{BC}$. If $m$ is the smallest possible value of $x$, find $m^2$.

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