
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  $ABC$  be a right triangle with a right angle at  $C.$  Two lines, one parallel to  $AC$  and the other parallel to  $BC,$  intersect on the hypotenuse  $AB.$  The lines split the triangle into two triangles and a rectangle. The two triangles have areas  $512$  and  $32.$  What is the area of the rectangle?

*Author: Ray Li*

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