
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 $N$ be the midpoint of side $AC$ of triangle $ABC$. Let $Q$ be a point on segment $AC$ between $A$ and $N$, and let $NE$ be drawn parallel to $QB$ and intersecting $AB$ at $E$. Determine the ratio, $s$, of the area of triangle $AQB$ to that of triangle $ABC$.
A) $s = \frac{1}{3}$, independent of the position of Q
B) $0 < s \leq \frac{1}{2}$, depending upon the position of Q
C) $\frac{1}{3} \le s < \frac{2}{3}$, depending upon the position of Q
D) $s = \frac{1}{2}$, independent of the position of Q

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