
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
The sequence $\{a_n\}$ is defined such that $a_1=3$ and $a_n - a_n a_{n+1} = 1$ for $n \in \mathbb{N^*}$. Let $A_n$ represent the product of the first $n$ terms of the sequence $\{a_n\}$. Find the value of $A_{2017}$.

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