
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
Line segment  $\overline{AB}$  has perpendicular bisector  $\overline{CD}$ , where  $C$  is the midpoint of  $\overline{AB}$ . The segments have lengths  $AB = 72$  and  $CD = 60$ . Let  $R$  be the set of points  $P$  that are midpoints of line segments  $\overline{XY}$  , where  $X$  lies on  $\overline{AB}$  and  $Y$  lies on  $\overline{CD}$ . Find the area of the region  $R$ .

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