
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 $f(x) = 2a\ln x - x^2$.
1. If $a=2$, find the equation of the tangent line to the graph of $f(x)$ at the point $(1, f(1))$.
2. If $a > 0$, determine whether the function $f(x)$ has a maximum or minimum value on its domain. If it does, find the maximum or minimum value of $f(x)$.

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