
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 diameters of a circle with a radius of 6 that intersect at right angles at point $O$. The points $B$ and $D$ are on the horizontal diameter, and $A$ and $C$ are on the vertical diameter. Given that $\triangle OAC$ is an isosceles right triangle, find the area of the shaded regions, which include $\triangle OBD$, $\triangle OAC$, and two quarter-circle sectors: $OAB$ and $OCD$.

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