
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
Lucas, Mia, and Grace are planning a hike. Lucas hikes at a speed of 5 miles per hour. If Mia hikes $\frac{3}{4}$ as fast as Lucas, and Grace hikes $\frac{6}{7}$ as fast as Mia, how fast does Grace hike? Additionally, if Liam hikes $\frac{4}{3}$ times faster than Grace, determine Liam’s hiking speed.

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