
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
Given that $BDEF$ is a rectangle and $AB = BC = 2$. Square $BDEF$ is surrounded by an additional rectangle whose one side equals two times the side of square $BDEF$ and another side equals the side of the square itself. Calculate the total area of the shape composed of the rectangle and square minus the area of a regular octagon inscribed in square $BDEF$.

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