
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 at 0 on a number line and aims to reach the point 2, but his hopping strategy alternates. On odd-numbered hops, he covers $\frac{1}{2}$ of the distance to his goal, while on even-numbered hops, he covers $\frac{1}{4}$ of the distance remaining to the goal. Determine the total distance Kevin hops after six hops. Express your answer as a fraction.

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