
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
Let \( c \) and \( k \) be constants. Consider the simultaneous equations:
\[
x - 2y = 4,
\]
\[
cx + 3y = k.
\]
Find the conditions on \( c \) and \( k \) such that the solution \((x, y)\) lies in Quadrant I.
**A)** \( c > -\frac{3}{2} \) and \( k > \max(-6, 4c) \)
**B)** \( c < -\frac{3}{2} \) or \( k < \min(-6, 4c) \)
**C)** \( c > 0 \) and \( k < -6 \)
**D)** \( c > -\frac{3}{2} \) and \( k > 4c \)

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