
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
It is known that the number \( e \) (the base of natural logarithms) is defined as the limit of the expression \(\left(1+\frac{1}{n}\right)^{n}\) as \( n \) increases without bound:

\[ e=\lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^{n} \]

However, one might reason as follows: if the exponent of a base that is slightly more than 1 increases without bound, then the power should also increase without bound, so \( e=\infty \). Alternatively, as \( n \) approaches infinity, \(\frac{1}{n}\) becomes zero, thus \(1+\frac{1}{n}\) becomes one, and any power of 1 is 1; therefore, \( e=1 \). Yet, it is claimed that the transcendental number \( e=2.71828 \ldots \). Where is the truth?

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