
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 function $f(x)= \begin{cases} 1-\sin x,x\in[0,\pi) \\ \log_{2016} \frac {x}{\pi},x\in[\pi,+\infty)\end{cases}$, if there are three different real numbers $x_{1}$, $x_{2}$, $x_{3}$ ($x_{1} < x_{2} < x_{3}$), such that $f(x_{1})=f(x_{2})=f(x_{3})$, then the probability of the event satisfying $x_{1}+x_{2} > 4\pi-x_{3}$ is _____.

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