
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 function $f(x)= \frac{2}{x+1}$, point $O$ is the origin, point $A_n(n,f(n))$ where $n\in{N}^*$, vector $\vec{j}=(0,1)$, $\theta_n$ is the angle between vector $\overrightarrow{OA_n}$ and $\overrightarrow{j}$, calculate the value of $\frac{\cos \theta_1}{\sin \theta_1}+ \frac{\cos \theta_2}{\sin \theta_2}+ \frac{\cos \theta_1}{\sin \theta_1}+\cdots+ \frac{\cos \theta_{2016}}{\sin \theta_{2016}}$.

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