
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 power function $f(x)=x^{-k^{2}+k+2}$ $(k\in \mathbb{Z})$ satisfies $f(2) < f(3)$, and the function $g(x)=1-q$, $f(x)+(2q-1)x$ is a decreasing function on the interval $[-1,2]$, then the range of values for the non-negative real number $q$ is \_\_\_\_\_\_.

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