
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 point $P\left(m,n\right)$ is a point on the graph of the function $y=ax^{2}-4a^{2}x-3$ (where $a$ is a constant and $a\neq 0$), when $0\leqslant m\leqslant 4$ and $n\leqslant -3$, determine the range of values for $a$.

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