
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 an ellipse $C: \frac {x^{2}}{4}+ \frac {y^{2}}{3}=1$, its left and right vertices are $A_{1}$ and $A_{2}$ respectively, and for a point $P$ on $C$, the slope of the line $PA_{2}$ lies within the range $[-2,-1]$. Determine the range of the slope of the line $PA_{1}$.

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