
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]


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Three mutually tangent circles of radius $\sqrt{2}$ are located on the surface of a sphere with radius 2. The part of the sphere's surface that lies outside these circles consists of two curvilinear triangles. Find the areas of these triangles.

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