
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 new arrangement, lets consider a similar configuration where $ADB$ and $BEC$ are semicircles centered at point $B$ with radii 2 units and 3 units respectively, and point $D$, point $E$ are the midpoints of arc $ADB$, arc $BEC$. If arc $DFE$ is a semicircle centered on $F$ with a new radius of 2.5 units, find the area of the shaded region formed between these three semicircles, assuming overlaps occur at points $D$ and $E$.

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