
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
Ed and Sue both bike, jog, and swim at equal and constant rates. Ed covers a total of 86 kilometers after biking for 3 hours, jogging for 4 hours, and swimming for 2 hours. Sue, on the other hand, covers 110 kilometers after biking for 5 hours, jogging for 2 hours, and swimming for 4 hours. Determine the sum of the squares of their biking, jogging, and swimming rates. Assume all rates are whole numbers of kilometers per hour.

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