
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 $S_n$ is the sum of the first $n$ terms of the sequence $\{a_n\}$, with $a_1 = a_2 = 1$, and in the plane, there are three non-collinear vectors $\overrightarrow{OA}$, $\overrightarrow{OB}$, $\overrightarrow{OC}$, satisfying $\overrightarrow{OC} = (a_{n-1} + a_{n+1}) \overrightarrow{OA} + (1 - a_n) \overrightarrow{OB}$ for $n \geq 2$, $n \in \mathbb{N}^*$. If points $A$, $B$, and $C$ are collinear, then find $S_{2018}$.

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