
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, $C$ and $D$, start at the same time to ride from town X to town Y and town Z respectively, where town Y is $90$ miles away from X and town Z is $120$ miles away. Cyclist $C$ travels $6$ mph slower than cyclist $D$, who reaches town Y and then travels $30$ miles further before meeting cyclist $C$, who is still en route to town Y. Determine the speed of cyclist $C$.

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