
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 cycle, jog, and swim at equal and constant rates. Ed covers 80 kilometers after cycling for 3 hours, jogging for 2 hours, and swimming for 2 hours, while Sue covers 104 kilometers after jogging for 3 hours, swimming for 2 hours, and cycling for 4 hours. All their rates for cycling, jogging, and swimming are whole numbers in kilometers per hour. Determine the sum of the squares of Ed's cycling, jogging, and swimming rates.

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