
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 the diagram, $AB$ and $CD$ are perpendicular diameters of a circle with a radius of 5. Two quarter circle arcs are drawn within the circle: one from $A$ to $B$ passing through $O$, and the other from $C$ to $D$ passing through $O$. Calculate the area of the shaded region formed by the intersection of the quadrants and the inner quarter circle arcs.

[Your diagram here would show a circle with perpendicular diameters $AB$ and $CD$, and arc \(AB\) and arc \(CD\) drawn as quarter circles inside the main circle.]

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