
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 $f(x) = x^{\alpha}$ whose graph passes through the point $(4, 2)$, let $a_n = \frac{1}{f(n+1) + f(n)}$, where $n \in \mathbb{N}_+$, and denote the sum of the first $n$ terms of the sequence $\{a_n\}$ as $S_n$, then $S_{2017}=$ ?

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