
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 the following system of equations:
\begin{align*}
x - 2y &= 4, \\
2cx + y &= 5,
\end{align*}
determine the range of the constant $c$ such that the solution $(x, y)$ lies in Quadrant I.
**A)** $-\frac{1}{4} < c < \frac{13}{4}$  
**B)** $-\frac{1}{4} < c < \frac{5}{8}$  
**C)** $0 < c < \frac{3}{2}$  
**D)** $c > -\frac{1}{4}$  
**E)** $c < \frac{5}{8}$

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