
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 that $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ are two points on the parabola $y=ax^{2}-3x+1$, and their axis of symmetry is the line $x=x_{0}$. If $|x_{1}-x_{0}| \gt |x_{2}-x_{0}|$, then $y_{1} \gt y_{2}$. In the same coordinate system, we have $M(-1,-2)$ and $N(3,2)$, and the parabola $y=ax^{2}-3x+1$ intersects the line segment $MN$ at two distinct points. Find the range of values for $a$.

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