
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
Znayka cut out a semicircle from paper. Neznayka marked a point \(D\) on the diameter \(AB\) of this semicircle and cut out two semicircles with diameters \(AD\) and \(DB\) from Znayka's semicircle. Find the area of the remaining shape if the length of the chord passing through point \(D\) perpendicular to \(AB\) inside the remaining shape is 6. If necessary, round the answer to two decimal places.

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