
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
Let the function $f(x) = \frac{1}{2}x^2 - m\ln{x}$, and $g(x) = x^2 - (m+1)x$, where $m > 0$.
(1) Find the intervals of monotonicity for the function $f(x)$.
(2) When $m \geq 1$, discuss the number of intersection points between the graphs of $f(x)$ and $g(x)$.

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