
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
Consider the following equations:
$$ \cos\theta + i\sin\theta = a_1 + b_1i, $$
$$ (\cos\theta + i\sin\theta)^2 = a_2 + b_2i, $$
$$ (\cos\theta + i\sin\theta)^3 = a_3 + b_3i, $$
$$ \ldots $$
$$ (\cos\theta + i\sin\theta)^n = a_n + b_ni, $$
where $i$ is the imaginary unit, and $a_n, b_n$ ($n \in \mathbb{N}^*$) are real numbers. By induction, it can be determined that when $\theta = \frac{\pi}{2}$, the value of $a_{2016} + b_{2016}$ is _____.

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