
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
Tom and Jerry bike, jog, and swim at equal and constant rates. They spend different amounts of time on each activity but complete the same set of activities. Tom bikes for 3 hours, jogs for 1 hour, and swims for 5 hours, covering a total of 89 kilometers. Jerry bikes for 4 hours, jogs for 3 hours, and swims for 2 hours, covering a total of 106 kilometers. Their biking, jogging, and swimming rates are whole numbers in kilometers per hour. Find the sum of the squares of Tom's biking, jogging, and swimming rates.

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