
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 $\dfrac{x^{2}}{9} + \dfrac{y^{2}}{5} = 1$, let $F$ be the left focus, point $A$ be the right vertex, and point $P$ be on the ellipse, such that $FP$ is perpendicular to $PA$. Determine the slope of line $PF$.

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