
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
Point $A$ is the right vertex of the ellipse $C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>1)$, and point $P$ is a point on the ellipse $C$ (not coinciding with $A$), with coordinates $(a \cos \theta, b \sin \theta)$, where $\theta \neq \frac{\pi}{2}$. Determine the range of values for the eccentricity of the ellipse $C$ given that $\overrightarrow{PO} \cdot \overrightarrow{PA}=0$.

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