
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 the sequence $\{a_n\}$ is an arithmetic sequence, and the sequence $\{b_n\}$ is a geometric sequence, satisfying: $a_{1000}+a_{1018}=2\pi$, $b_{6}b_{2012}=2$, then $\tan \frac {a_{2}+a_{2016}}{1+b_{3}b_{2015}}=$ ______.

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