
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 curve $y = (a-3)x^3 + \ln x$ has a tangent line perpendicular to the y-axis, and the function $f(x) = x^3 - ax^2 - 3x + 1$ is monotonically increasing on the interval $[1,2]$, then the range of values for $a$ is ______.

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