
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

For \(1 \leq j \leq 2014\), define
\[ b_{j} = j^{2014} \prod_{i=1, i \neq j}^{2014} \left(i^{2014} - j^{2014}\right) \]
where the product is over all \(i \in \{1, \ldots, 2014\}\) except \(i = j\). Evaluate
\[ \frac{1}{b_{1}} + \frac{1}{b_{2}} + \cdots + \frac{1}{b_{2014}} .\]

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