
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 cycle, jog, and swim at constant rates. Ed covers 66 kilometers biking for 3 hours, jogging for 2 hours, and swimming for 4 hours, while Sue covers 96 kilometers after jogging for 3 hours, swimming for 2 hours, and biking for 4 hours. Their cycling, jogging, and swimming rates are all whole numbers of kilometers per hour. Find the sum of the squares of Ed's cycling, jogging, and swimming rates.

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