
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 ball with a radius of 1 cm was dipped in red paint and then placed between two perfectly smooth concentric spheres with radii of 4 cm and 6 cm respectively (the ball ended up outside the smaller sphere but inside the larger one). When the ball comes into contact with both spheres, it leaves a red mark. During its motion, the ball traced a closed path, resulting in a region outlined by a red contour on the smaller sphere, with an area of 47 square cm. Find the area of the region outlined by the red contour on the larger sphere. Give the answer in square centimeters, rounded to hundredths if necessary.

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