
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 the function $y=f(x)$ has a domain of $(0,+\infty)$, and when $x > 1$, $f(x) > 0$. For any $x$, $y\in(0,+\infty)$, the equation $f(x)+f(y)=f(xy)$ holds. If the sequence $\{a_n\}$ satisfies $a_1=f(1)$, and $f(a_{n+1})=f(2a_n+1)$ for $n\in\mathbb{N}^*$, find the value of $a_{2017}$.

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