
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 $C$: $\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$ ($a > 0, b > 0$) with asymptotic line equations $y = \pm \sqrt {3} x$ and the right vertex at $(1, 0)$:
(I) Find the equation of hyperbola $C$;
(II) A straight line $y = x + m$ intersects the hyperbola $C$ at two distinct points $A$ and $B$, with the midpoint of segment $AB$ being $M(x_0, y_0)$. When $x_0 \neq 0$, find the value of $\frac {y_0}{x_0}$.

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