
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 a function $y=f(x)$ with domain $\mathbb{R}$, where $f(x) > 1$ when $x < 0$, and for any real number $x$, $y \in \mathbb{R}$, the equation $f(x)f(y) = f(x+y)$ always holds. If the sequence $\{a_n\}$ satisfies $a_1 = f(0)$, and $f(a_{n+1}) = \frac{1}{f(-2-a_n)}$ for $n \in \mathbb{N^*}$, determine the value of $a_{2018}$.

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