
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 $A(-4, y_{1})$, $B(-3, y_{2})$, $C(0, y_{3})$, $D(2, y_{4})$ lie on the graph of the quadratic function $y=ax^{2}+4ax-6$. If among the four numbers $y_{1}$, $y_{2}$, $y_{3}$, $y_{4}$, only one number is greater than $0$, determine the range of values for $a$.

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