
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 \(d\) be a constant. The simultaneous equations are given by
\[
x-2y = 5,
\]
\[
dx + y = 6.
\]
Determine the value of \(d\) for which the solution \((x, y)\) lies in the first quadrant.
A) \(d = -\frac{1}{2}\)
B) \(-\frac{1}{2} < d < \frac{6}{5}\)
C) \(d < \frac{6}{5}\)
D) \(0 < d < 2\)
E) \(-1 < d < 1\)

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