
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 it is known that $$a_{2015}+a_{2017} = \int_{0}^{2} \sqrt{4-x^2}\,dx$$, find the minimum value of $a_{2016}(a_{2014}+a_{2018})$.

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