
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 cyclists started simultaneously from the same location in the same direction. Ten minutes later, a third cyclist started from the same location. He first overtook the first cyclist, and then continued riding for an additional 20 minutes until he caught up with the second cyclist. Each cyclist maintained a constant speed from start to finish: $a$ km/h for the first cyclist, and $b$ km/h for the second cyclist. Find the speed of the third cyclist.

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