
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
In a circle with radius \( R \), two perpendicular chords intersect each other.

a) Find the sum of the squares of the four segments into which these chords are divided by their point of intersection.

b) Find the sum of the squares of the lengths of the chords if the distance from the center of the circle to their point of intersection is \( d \).

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