
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 $f(x) = \frac{1}{x+1}$, let point $A\_0$ represent the origin, and point $A\_n(n, f(n)) (n \in \mathbb{N}^*)$. If vector $a\_n = \overset{→}{A\_0A\_1} + \overset{→}{A\_1A\_2} + \cdots + \overset{→}{A\_{n-1}A\_n}$, and $\theta\_n$ is the angle between $a\_n$ and $i$ (where $i = (1, 0)$), calculate the value of $\tan \theta\_1 + \tan \theta\_2 + \tan \theta\_3$.

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