
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 run, bicycle, and roller-skate at equal and constant rates. They both spend different amounts of time on each activity, yet the overall distance they cover is equal due to their constant rates in each activity. Tom runs for $3$ hours, bicycles for $4$ hours, and roller-skates for $2$ hours, covering a total of $104$ kilometers. Jerry rolls-skates for $2$ hours, bicycles for $6$ hours, and runs for $3$ hours, covering a total of $140$ kilometers. Determine the sum of the squares of Tom's running, bicycling, and roller-skating rates assuming all rates are whole numbers of kilometers per hour.

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