
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
Let \(\mathbb{N}\) denote the set of positive integers. Let \(\varphi: \mathbb{N} \rightarrow \mathbb{N}\) be a bijective function and assume that there exists a finite limit

$$
\lim _{n \rightarrow \infty} \frac{\varphi(n)}{n} = L
$$

What are the possible values of \(L\)?

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