
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
Two checkpoints divide a ski track into three segments of equal length. It is known that the skier covered the first and second segments together at an average speed of $a$ meters per minute; the skier covered the second and third segments together at an average speed of $b$ meters per minute. The average speed of the skier on the second segment was the same as the average speed for the first and third segments together. What is the average speed of the skier on the entire track and on each segment of the track individually? Analyze the conditions for the existence of a real solution to the problem.

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