
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 an ellipse $C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$, $P$ is a point on the ellipse $C$, $F_{1}(-c,0)$, $F_{2}(c,0)$ are the left and right foci of the ellipse $C$. If $\overrightarrow{PF_1} \cdot \overrightarrow{PF_2} \leq ac$ always holds, determine the range of eccentricity $e$ of the ellipse $C$.

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