
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 a hyperbola $C$ with its vertices on the $x$-axis, the distance between the two vertices is $8$, and the eccentricity $e= \frac {5}{4}$.
(1) Find the standard equation of the hyperbola $C$;
(2) A line passing through the point $P(3,0)$ with a slope of $k$ intersects the hyperbola $C$ at exactly one point. Find the value of $k$.

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