
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
A rectangle with side lengths $2$ and $4$, a square with side length $1$, and a rectangle $R$ are inscribed inside a larger square. The square and the rectangle are positioned such that each of them shares at least one side with the boundary of the larger square. Determine the sum of all possible values for the area of $R$.

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