
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 smooth sphere with a radius of 1 cm is dipped in blue paint and placed between two absolutely smooth concentric spheres with radii of 4 cm and 6 cm, respectively (this sphere is outside the smaller sphere but inside the larger one). Upon contact with both spheres, the smaller sphere leaves a blue mark. During its movement, the sphere traced a closed path, resulting in a region on the smaller sphere outlined in blue paint, with an area of 17 square cm. Find the area of the region outlined in blue on the larger sphere. Give the answer in square centimeters, rounding to the nearest hundredth if necessary.

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