
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
A function $f(x)$ is defined on the set of real numbers $\mathbb{R}$ and satisfies the equation:

$$f(\tan x) = \frac{1}{\cos 2x}$$

Find the sum of the values of this function for the following arguments:

$$f\left(\frac{1}{2016}\right) + f\left(\frac{1}{2015}\right) + \dots + f\left(\frac{1}{2}\right) + f(0) + f(2) + \dots + f(2015) + f(2016) = \_\_\_\_\_\_\_$$

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