
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

Find the sum of the squares of the distances from a point \( M \), taken on the diameter of some circle, to the ends of any chord parallel to this diameter, if the radius of the circle is \( R \) and the distance from point \( M \) to the center of the circle is \( a \).

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