
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 $f(x)= \frac {1}{2}ax^{2}-(2a+1)x+2\ln x$.  
$(1)$ If the tangents of the function $y=f(x)$ at $x=1$ and $x=3$ are parallel, find the value of $a$;  
$(2)$ If $a > 0$, find the intervals where the function $y=f(x)$ is increasing.

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