
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 $\frac{x^2}{4} + y^2 = 1$, let $F_1$ and $F_2$ represent the left and right foci, respectively, and let $P$ be a moving point on the ellipse. If $\angle F_1 P F_2$ is an obtuse angle, find the range of possible values for the x-coordinate of point $P$.

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