
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 $f(x) = x^3 - 3x$, where $x \in \mathbb{R}$, the equation of the tangent line to the curve $y = f(x)$ at the point $P(x, f(x))$ is $y = g(x)$. Let $h(x) = f(x) - g(x)$.

(I) If $x = 2$, find the expression for the function $h(x)$.

(II) If $x \in \mathbb{R}$, discuss the monotonicity of the function $h(x)$.

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