
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 $\mathbb{R}$, when $x < 0$, $f(x) > 1$, and for any real numbers $x, y \in \mathbb{R}$, 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