
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 $f(x)=\ln x+ax^{2}-(2a+1)x$, where $a\neq 0$.
(I) When $a=2$, find the equation of the tangent line at the point $(1,f(1))$;
(II) Find the monotonic intervals of $f(x)$;
(III) When $a > 0$, determine the number of zeros of the function $f(x)$. (Only the conclusion needs to be written out)

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