
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 the definition of a matrix transformation from vector $\overrightarrow{OP\_n} = (x\_n, y\_n)$ to vector $\overrightarrow{OP_{n+1}} = (x_{n+1}, y_{n+1})$ as follows:

$$\begin{pmatrix} x_{n+1} \\ y_{n+1} \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix} \begin{pmatrix} x_n \\ y_n \end{pmatrix},$$

where $O$ is the coordinate origin, $n \in \mathbb{N}^*$, and $\overrightarrow{OP\_1} = (2, 0)$, find the coordinates of $\overrightarrow{OP_{2016}}$.

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