
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 $C: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ with eccentricity $e= \frac{\sqrt{3}}{2}$, and points $A$ and $B$ being the left and right vertices of the ellipse respectively. Point $P$ is a point on the ellipse, and the angles of lines $PA$ and $PB$ are $α$ and $β$ respectively, satisfying $\tan α+\tan β=1$. Find the slope of line $PA$.

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