
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 $f(x)=\frac{1}{2}ax^2-(2a+1)x+2\ln x$ where $a\in\mathbb{R}$:
1. When $a=-1$, find the equation of the tangent line to $f(x)$ at the point $(1,f(1))$.
2. When $a>0$, determine the intervals where the function $f(x)$ is monotonically increasing.

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