
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
The vertices of the ellipse \\(C: \frac{x^2}{4} + \frac{y^2}{3} = 1\\) are \\(A_1\\) and \\(A_2\\). Point \\(P\\) is on \\(C\\) and the range of the slope of line \\(PA_2\\) is \\([-2, -1]\\). Determine the range of the slope of line \\(PA_1\\).

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