
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 $\zeta(s)=\sum_{n=1}^{\infty} n^{-s}$ be the Riemann zeta function $(1<s<\infty)$. Euler's formula states that $\zeta(s)$ has the following representation:

$$
\zeta(s)=\prod_{n=1}^{\infty}\left(1-\frac{1}{p_{n}^{s}}\right)^{-1}
$$

where $p_{1}, p_{2}, \ldots$ is the sequence of prime numbers greater than one. Provide a proof for this result.

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