
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
An ellipse (C) with the equation $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ has an eccentricity of $\frac{\sqrt{6}}{3}$, and the distance from one endpoint of the minor axis to the right focus is $\sqrt{3}$.
(1) Find the equation of ellipse (C);
(2) If line $y=x+1$ intersects with ellipse (C) at points A and B, find the distance between A and B.

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