
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 sphere $g$ has chords $h_{1}, h_{2},$ and $h_{3}$ passing through a fixed internal point $P$ and are mutually perpendicular to each other. The three planes defined by these chords each intersect the sphere in a circle. Demonstrate that the sum of the areas of these three circles does not depend on the positions of the chords.

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