
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 eccentricity of an ellipse (C) with its focus on the x-axis and center at the origin is $\frac{4}{5}$, and it passes through the point $(\frac{10\sqrt{2}}{3}, 1)$.
(I) Find the equation of the ellipse (C);
(II) Line (l) cuts the ellipse (C) and the circle (M): $x^2+y^2=R^2$ (where $3 < R < 5$) at points A and B. Find the maximum value of $|AB|$.

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