
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 place in the same direction. Ten minutes later, a third cyclist began his journey from the same place. First, he overtook the first cyclist, and then after traveling for another 20 minutes, he caught up with the second cyclist. From the start to the end of the journey, each cyclist traveled at a constant speed of $a$ km/h for the first cyclist and $b$ km/h for the second. Find the speed of the third cyclist.

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