
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 bike at equal and constant rates. Similarly, they jog and swim at equal and constant rates respectively. Ed covers 112 kilometers after biking for 3 hours, jogging for 2 hours, and swimming for 2 hours, while Sue covers 129 kilometers after biking for 2 hours, jogging for 3 hours, and swimming for 4 hours. Their biking, jogging, and swimming rates are all whole numbers of kilometers per hour. Find the sum of the squares of Ed's and Sue's biking, jogging, and swimming rates.

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