
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 that the function $f(x) = x^2 + bx$ has its tangent line at point $A(1, f(1))$ parallel to the line $3x - y + 2 = 0$, and let the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{f(n)} \right\}$ be $S_n$, determine the value of $S_{2014}$.

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