
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 \\(f(x)=|x-2017|+|x-2016|+\ldots+|x-1|+|x+1|+\ldots+|x+2017| (x \in \mathbb{R})\\), and it satisfies \\(f(a^{2}-3a+2)=f(a-1)\\) for integer \\(a\\) with a total of \\(n\\) values, \\(g(x)= \dfrac {x^{2}(x^{2}+k^{2}+2k-4)+4}{(x^{2}+2)^{2}-2x^{2}}\\)'s minimum value is \\(m\\), and \\(m+n=3\\), then the value of the real number \\(k\\) is \_\_\_\_\_\_.

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