
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
Eugene, Claire, and Liam are planning a cycling trip. Eugene cycles at a rate of 6 miles per hour. If Claire cycles $\frac{3}{4}$ as fast as Eugene, and Liam cycles $\frac{4}{3}$ as fast as Claire, how fast does Liam cycle?

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