
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 sequence $\left\{u_{n}\right\}$ is defined as follows:
$$
u_{1}=1, \quad u_{n+1}=\left(\sum_{k=1}^{n} u_{k}\right)^{-1}.
$$

Question: Do there exist constants $\alpha$ and $\beta$ such that
$$
\lim _{n \rightarrow +\infty} \frac{u_{1} + u_{2} + \cdots + u_{n}}{\alpha n^{\beta}} = 1?
$$

If such constants exist, determine $\alpha$ and $\beta$. If they do not exist, provide reasoning.

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