
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
After one third of the water is poured out, the remaining water is $\frac{2}{3}$ of the original amount. Then, one fourth of the remainder is poured out, and the remaining water is $\frac{3}{4} \cdot \frac{2}{3} = \frac{1}{2}$ of the original amount. This process continues with one fifth of the remainder for the third pouring, one sixth for the fourth, and so forth. After the $n$th pouring, the remaining water is $\left( \frac{2}{3} \right) \left( \frac{4}{5} \right) \left( \frac{5}{6} \right) \left( \frac{6}{7} \right) \cdots \left( \frac{n+2}{n+1} \right)$ of the original amount.

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