
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
1. Construct a right-angled quadrilateral (e.g., from paper) that remains similar in shape when folded so that its shorter sides overlap.

2. a) Construct a right-angled quadrilateral that remains similar in shape when a square constructed over the shorter side is cut off.

   b) Starting with such a quadrilateral, consider the process described in part a) indefinitely and determine the sum of the areas of the resulting right-angled quadrilaterals.

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