
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 $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$, where the sum of the distances from any point on the ellipse to the two foci $F_{1}$ and $F_{2}$ is $4\sqrt{2}$, and the eccentricity is $\frac{\sqrt{3}}{2}$.<br/>$(1)$ Find the standard equation of the ellipse;<br/>$(2)$ Find the length of the major axis, coordinates of the foci, and the equation of the directrix.

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