
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
Rectangle \( R_{0} \) has sides of lengths 3 and 4. Rectangles \( R_{1}, R_{2} \), and \( R_{3} \) are formed such that:
- all four rectangles share a common vertex \( P \),
- for each \( n=1,2,3 \), one side of \( R_{n} \) is a diagonal of \( R_{n-1} \),
- for each \( n=1,2,3 \), the opposite side of \( R_{n} \) passes through a vertex of \( R_{n-1} \) such that the center of \( R_{n} \) is located counterclockwise of the center of \( R_{n-1} \) with respect to \( P \).

Compute the total area covered by the union of the four rectangles.

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