
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 a line $l: x+y-4=0$, let $M$ be any point on the line. If an ellipse is drawn through $M$ with one of its foci being a focus of the ellipse $\frac{x^{2}}{16}+ \frac{y^{2}}{12}=1$, determine the minimum length of the major axis of such an ellipse.

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