
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 $D$ is the triangular region (including the boundary and interior) with vertices at points $A(4,1)$, $B(-1,-6)$, and $C(-3,2)$.

$(1)$ Write the system of inequalities representing region $D$.

$(2)$ Given that points $B(-1,-6)$ and $C(-3,2)$ are on opposite sides of the line $4x-3y-a=0$, find the range of values for $a$.

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