
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
Examine the following equations:
\begin{align*}
\cos \theta + i \sin \theta &= a\_1 + b\_1 i, \\
(\cos \theta + i \sin \theta)^2 &= a\_2 + b\_2 i, \\
(\cos \theta + i \sin \theta)^3 &= a\_3 + b\_3 i, \\
&\vdots \\
(\cos \theta + i \sin \theta)^n &= a\_n + b\_n i,
\end{align*}
where $i$ is the imaginary unit, and $a\_n$, $b\_n (n \in \mathbb{N}^*)$ are real numbers. By induction, find the value of $a\_{2016} + b\_{2016}$ when $\theta = \frac{\pi}{2}$.

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