
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 \\(f(x)= \begin{cases} -2x-2, & x\in (-\infty ,0) \\ x^{2}-2x-1, & x\in [0,+\infty ) \end{cases}\\), and \\(x_{1}\leqslant x_{2}\leqslant x_{3}\\), with \\(f(x_{1})=f(x_{2})=f(x_{3}\\). Determine the range of values for \\(x_{1}+x_{2}+x_{3}\\).

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