
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 $P(-2, y_{1})$, $Q(4, y_{2})$, $M(m, y_{3})$ are all on the parabola $y=ax^{2}+bx+c$, where $2am+b=0$. If $y_{3}\geqslant y_{2} \gt y_{1}$, determine the range of values for $m$.

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