
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
Given the sequence \( \{a_{n}\} \) satisfying:
\[
\begin{array}{l}
a_{1} = e, a_{2} = e^3, \\
e^{1-k} a_{n}^{k+2} = a_{n+1} a_{n-1}^{2k} \quad (n \geqslant 2, n \in \mathbf{Z}_{+}, k \in \mathbf{R}_{+})
\end{array}
\]
Find the product \(\prod_{i=1}^{2017} a_{i}\).

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