
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 $f(x)= \frac{2x}{x+1}$, calculate the value of the expression $f\left( \frac{1}{2016}\right)+f\left( \frac{1}{2015}\right)+f\left( \frac{1}{2014}\right)+\ldots+f\left( \frac{1}{2}\right)+f(1)+f(2)+\ldots+f(2014)+f(2015)+f(2016)$.

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