
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 the right focus of the hyperbola $\frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1(a>0,b>0)$ is point F, the eccentricity is $\frac{5}{3}$, and the distance from point F to one asymptote of the hyperbola is 4. Determine the equation of the hyperbola.

A) $\frac{x^{2}}{9}- \frac{y^{2}}{16}=1$
B) $\frac{x^{2}}{16}- \frac{y^{2}}{9}=1$
C) $\frac{x^{2}}{25}- \frac{y^{2}}{16}=1$
D) $\frac{x^{2}}{25}- \frac{y^{2}}{9}=1$

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