
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 $f(x)=\frac{1}{2}ax^2 - 2\ln{x}$, where $a \in \mathbb{R}$.
(1) Find the monotonic intervals of the function $f(x)$;
(2) Given point $P(0, 1)$ and a moving point $M(m, f(m))$ on the graph of function $f(x)$, for any $m \in [1, e]$, the angle of line $PM$ is always obtuse. Find the range of values for $a$.

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