
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
$ABCD$ is an isosceles trapezoid with bases $AB = 92$ and $CD = 19$. The length of $AD = BC = x$. A circle centered on $AB$ is tangent to $AD$ and $BC$. Find the value of $m^{2}$, where $m$ is the minimum value of $x$.

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