
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 a trapezoid with $AB=8$ (non-parallel to $CD$), $BC=7=DA$, and $CD=6$. Circles of radius 4 are centered at $A$ and $B$, and circles of radius 3 are centered at $C$ and $D$. Find the radius of a smaller circle that fits exactly inside the trapezoid touching all four circles.

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