
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
A woman carried water from the well to the kitchen in a straight cylindrical bucket. The bucket had a hole on the side at a height of $\frac{1}{4}$ of the bucket's height from the bottom, causing half of the water to leak out on her way from the well to the kitchen. After she fixed this hole, the bottom of the bucket developed a hole, and $\frac{2}{3}$ of the water leaked out on the same journey. She fixed this hole too, but later both plugs failed, and by the time she was 1 meter away from the kitchen, only $\frac{1}{40}$ of the water was left in the bucket. How far was the well from the kitchen? (For simplicity, assume water leaks evenly over time from each hole.)

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