
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
Consider the ellipse (C) given by the equation $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$. Let $A\_1$ and $A\_2$ be the left and right vertices of the ellipse, respectively. Suppose point $P$ lies on the ellipse such that the slope of line $PA\_2$ is in the range $[-2, -1]$. Determine the range of possible slopes for line $PA\_1$.

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