
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 \( f(x) = \ln x - (a+2)x + ax^2 \) where \( a \in \mathbb{R} \).
- (I) When \( a = 0 \), find the equation of the tangent line to the curve \( y = f(x) \) at the point \((1, f(1))\).
- (II) Find the intervals where \( f(x) \) is monotonic.
- (III) If \( f(x) \) has exactly two zeros, find the range of real number \( a \).

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