
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
Inside a sphere of radius \( R \), there is a point \( A \) at a distance \( a \) from its center. Through point \( A \), three mutually perpendicular chords are drawn.

a) Find the sum of the squares of the lengths of these chords.

b) Find the sum of the squares of the lengths of the segments of these chords, created by point \( A \).

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