
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 $f(x) = x^3 - ax^2 + bx + c$.
- (I) If $a=3$, $b=-9$, find the intervals of monotonicity for $f(x)$.
- (II) If there exists a point $P$ on the graph of $y=f(x)$ such that the tangent line at point $P$ is parallel to the x-axis, find the relationship between the real numbers $a$ and $b$.

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