
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
 $f$  is a differentiable  function such that  $f(f(x))=x$  where  $x \in [0,1]$ .Also  $f(0)=1$ .Find the value of   $$ \int_0^1(x-f(x))^{2016}dx $$  

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