
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
An elastic ball falls from a height of 128m, where each bounce reaches half of its previous height before falling again. Calculate the total distance traveled by the ball when it hits the ground for the 8th time.

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