
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
Three runners start simultaneously from the same point on a 800-meter circular track and run at constant speeds of 4.5, 5.0, and 5.5 meters per second, respectively, and run clockwise around the track. Having run for t seconds, let x, y, and z be the distances traveled by the three runners, respectively. The runners will meet again after traveling a total distance of 800 meters, so x + y + z = 800. Express x, y, and z as multiples of their respective speeds to form the equation 4.5t + 5.0t + 5.5t = 800.

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