
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
(The full score of this question is 12 points)  
It is known that the function $f(x) = ax^2 + b\ln x$ has an extremum at $x = 1$.  
(1) Find the values of $a$ and $b$;  
(2) Determine the monotonicity of the function $y = f(x)$ and find the monotonic intervals.

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