
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 the function $f(x)=\frac{a^{x}}{a^{x}+\sqrt{a}}\ (a>0)$, if $x\_1+x\_2=1$, then $f(x\_1)+f(x\_2)=1$\_, and find $f(\frac{1}{2016})+...+f(\frac{2015}{2016})=$ \_\_\_\_\_\_.

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