
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 $k$ be a constant. The system of equations
\begin{align*}
x - y &= 4 \\
kx^2 + y &= 5
\end{align*}
has a solution $(x, y)$ in Quadrant I if and only if which of the following is true?
**A** $k > -\frac{1}{18}$   
**B** $k > -\frac{1}{36}$   
**C** $k < \frac{5}{3}$   
**D** $k = -\frac{1}{36}$

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