
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 that the left focus of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$ is $F(-c, 0)$, the eccentricity is $\frac{\sqrt{3}}{3}$, and point $M$ lies on the ellipse in the first quadrant. The line segment formed by the intersection of line $FM$ and the circle $x^{2} + y^{2} = \frac{b^{2}}{4}$ has a length of $c$, and $|FM| = \frac{4\sqrt{3}}{3}$.

(I) Find the slope of line $FM$.
(II) Find the equation of the ellipse.

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