
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 an ellipse $G: \frac{{x}^{2}}{4}+{y}^{2}=1$. A tangent line $l$ to the circle $x^{2}+y^{2}=1$ passes through the point $(m,0)$ and intersects the ellipse $G$ at points $A$ and $B$. Express $|AB|$ as a function of $m$. Then, determine the maximum value of $|AB|$.

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