
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 $f(x) = x^3 + (4-a)x^2 - 15x + a$, where $a \in \mathbb{R}$.
(I) If point P(0, -2) lies on the graph of the function $f(x)$, determine the value of $a$ and the minimum value of the function $f(x)$.
(II) If the function $f(x)$ is monotonically decreasing on the interval (-1, 1), find the maximum value of $a$.

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