
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
Kevin Kangaroo starts his hopping journey on a number line at 0 and aims to reach 2, but his first hop can only take him \(\frac{1}{4}\) of the distance. Subsequently, he gets tired and each subsequent hop spans only \(\frac{2}{3}\) of the remaining distance. Determine how far Kevin has hopped after six hops. Express your answer as a common fraction.

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