
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 $f(x)=\begin{cases} & \cos (x-\dfrac{\pi }{2}),x\in [0,\pi ] \\ & \log_{2015}\dfrac{x}{\pi },x\in (\pi ,+\infty ) \end{cases}$, if there are three different real numbers $a$, $b$, and $c$ such that $f(a)=f(6)=f(c)$, determine the range of values for $a+b+c$.

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