
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 the ellipse $G$: $\frac{x^{2}}{4}+y^{2}=1$. A circle $x^{2}+y^{2}=1$ is drawn through the point $(m, 0)$, and its tangent line $l$ intersects the ellipse $G$ at points $A$ and $B$.

(1) Find the coordinates of the foci and the eccentricity of the ellipse $G$;

(2) Express $|AB|$ as a function of $m$, and find the maximum value of $|AB|$

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