
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 ellipse \( E: \frac{x^{2}}{9}+\frac{y^{2}}{5}=1 \) with the left focus \( F_{1} \), a line \( l \) passing through \( F_{1} \) intersects the ellipse \( E \) at points \( A \) and \( B \). Point \( Q \left( -\frac{9}{2}, 0 \right) \) is given. If \( \overrightarrow{Q B} \perp \overrightarrow{A B} \), find the slope of the line \( l \).

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