
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 that $S$ is an infinite subset of the set of positive integers, satisfying the condition that for any $a, b, c \in S$, $a b c \in S$. Let the elements of $S$ be arranged in ascending order to form a sequence $\left\{a_{n}\right\}$, and it is known that $a_{1}=2$ and $a_{2031}=2^{4061}$. What is $a_{2017}$? ___ .

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