
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 line $l: (a+1)x + (3a-1)y - (6a+2) = 0$ and the ellipse $C: \frac{x^2}{16} + \frac{y^2}{m} = 1$, determine the range of real values for $m$ such that the line and the ellipse always have a common point.

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