
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 $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}} = 1$$ ($a, b > 0$) with a real axis length of $4\sqrt{3}$, and the distance from the focus to the asymptote is $\sqrt{3}$.

(1) Find the equation of this hyperbola;  
(2) It is known that the line $y= \frac{\sqrt{3}}{3}x-2$ intersects the right branch of the hyperbola at points A and B, and there exists a point C on the right branch of the hyperbola such that $\overrightarrow{OM} + \overrightarrow{OB} = m \overrightarrow{OC}$. Find the value of $m$ and the coordinates of point C.

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