
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
Consider a constant $k$. The simultaneous equations
\begin{align*}
x + 2y &= 6, \\
kx - y &= 2,
\end{align*}
must have solution $(x, y)$ in Quadrant I. Determine the range of $k$ for which this condition holds.
A) $k > 2$
B) $k > -\frac{1}{2}$
C) $k > \frac{1}{3}$
D) $k < \frac{1}{3}$

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