
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 function $f(x) = x^3 - ax^2 + 3x$.

(I) If $f(x)$ is an increasing function on $x \in [1, +\infty)$, find the range of values for the real number $a$.

(II) If $x = 3$ is an extreme point of $f(x)$, find the minimum and maximum values of $f(x)$ on $x \in [1, a]$.

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