
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 given by the equation $\frac{x^2}{4} + y^2 = 1$. Let $F_1$ and $F_2$ denote the left and right foci of the ellipse, respectively, and let $P$ be a moving point on the ellipse. If the angle $∠F_1PF_2$ is obtuse, then the range of possible values for the $x$-coordinate of $P$ is _______.

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