
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
The quadratic equation $g(x) = 3x^2 + 12x + d = 0$ is given, where $d$ is defined such that the graph of $y = g(x)$ is tangent to the x-axis. Identify the value of $d$, and determine the nature of the vertex (maximum or minimum).
A) d = 12, maximum
B) d = 12, minimum
C) d = 6, minimum
D) d = 6, maximum

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