
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 was dipped in blue paint and placed between two absolutely smooth concentric spheres with radii of 4 cm and 6 cm, respectively (the sphere was outside the smaller sphere but inside the larger one). When in contact with both spheres, the sphere leaves a blue trace. While moving, the sphere traveled along a closed path, resulting in a region on the smaller sphere outlined in blue with an area of 17 square centimeters. Find the area of the region outlined in blue on the larger sphere. Provide the answer in square centimeters, rounding to two decimal places if necessary.

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