
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 \( \mathrm{f}(x) \) is a polynomial of degree 2012, and that \( \mathrm{f}(k) = \frac{2}{k} \) for \( k = 1,2,3, \cdots, 2013 \), find the value of \( 2014 \times \mathrm{f}(2014) \).

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