
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
In a geometric layout, arc $ADB$ and arc $BEC$ are semicircles, each with a radius of 2 units. Points $D$, $E$, and $F$ are the midpoints of arc $ADB$, arc $BEC$, and arc $DFE$, respectively. Arc $DFE$ is also a semicircle but has a radius of 1 unit. Calculate the area of the shaded region formed by these arcs and points, assuming a similar configuration to the original problem.

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