
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]


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Given the hyperbola C with equation $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$, the shortest distance from a point on the hyperbola to one of its foci is 2. If point P(3, 4) lies on an asymptote of hyperbola C, find the equation of hyperbola C from the options below:
A) $$\frac{x^2}{16} - \frac{y^2}{9} = 1$$
B) $$\frac{x^2}{9} - \frac{y^2}{16} = 1$$
C) $$\frac{x^2}{4} - \frac{y^2}{3} = 1$$
D) $$\frac{x^2}{3} - \frac{y^2}{4} = 1$$

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