
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
**H**orizontal parallel segments  $AB=10$  and  $CD=15$  are the bases of trapezoid  $ABCD$ . Circle  $\gamma$  of radius  $6$  has center within the trapezoid and is tangent to sides  $AB$ ,  $BC$ , and  $DA$ . If side  $CD$  cuts out an arc of  $\gamma$  measuring  $120^{\circ}$ , find the area of  $ABCD$ .

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