
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: $\bullet$  all four rectangles share a common vertex  $P$ , $\bullet$  for each  $n = 1, 2, 3$ , one side of  $R_n$  is a diagonal of  $R_{n-1}$ , $\bullet$  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.
![Image](https://cdn.artofproblemsolving.com/attachments/3/1/e9edd39e60e4a4defdb127b93b19ab0d0f443c.png)

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