
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
Let the function $f(x)= \frac {1}{2}x^{2}+a\ln x$ ($a < 0$).  
(1) If the slope of the tangent line to the graph of $f(x)$ at the point $(2,f(2))$ is $\frac {1}{2}$, find the value of the real number $a$;  
(2) Determine the intervals of monotonicity for $f(x)$;  
(3) Let $g(x)=x^{2}-(1-a)x$, when $a\leqslant -1$, discuss the number of intersection points between the graphs of $f(x)$ and $g(x)$.

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