
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) In the diagram below, $ABCD$ is a square with side $4 \, \text{cm}$ and the shaded regions are enclosed by two semicircles with diameters $AB$ and $BC$. Calculate the area of the shaded region.

b) Given the square $ABCD$ with side length 2. Let $O$ be the center of the square, and $E$ and $F$ the midpoints of the sides $CD$ and $AB$ respectively. If the segments $FH$ and $GE$ have the same length and the arcs $FE, EH, HO, OG, FG$ are semicircles, find the shaded area.

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