
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
Let $y=f(x)$ be an even function on $\mathbb{R}$, satisfying $f(x+4)=f(4-x)$. When $x\in[0,4]$, $f(x)=x$ and $\sin α= \frac{ \sqrt {2}}{3}$, find the value of $f\left[2016+\sin (α-2π)⋅\sin (π+α)-2\cos ^{2}(-α)\right]$ .

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