
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 sequence $\{a\_n\}(n=1,2,3,...,2016)$, circle $C\_1$: $x^{2}+y^{2}-4x-4y=0$, circle $C\_2$: $x^{2}+y^{2}-2a_{n}x-2a_{2017-n}y=0$. If circle $C\_2$ bisects the circumference of circle $C\_1$, then the sum of all terms in the sequence $\{a\_n\}$ is $\_\_\_\_\_\_$.

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