
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 points $A(m, y_{1})$, $B(m+2, y_{2})$, and $C(x_{0}, y_{0})$ lie on the graph of the quadratic function $y=ax^{2}+4ax+c\left(a\neq 0\right)$, where $C$ is the vertex of the parabola. If $y_{0}\geqslant y_{2} \gt y_{1}$, find the range of values for $m$.

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