
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 that $F$ is the left focus of the ellipse $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a > b > 0)$, $A$ is the right vertex, and $P$ is a point on the ellipse such that $PF$ is perpendicular to the $x$-axis. If $\left| PF \right|=\frac{3}{4}\left| AF \right|$, what is the eccentricity of the ellipse?

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