
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 $f(x)= \frac {1}{2}ax^{2}-(a+1)x+\ln x$ $(a > 0)$, $x= \frac {1}{4}$ is a critical point of the function.  
$(1)$ Find the value of the real number $a$;  
$(2)$ Definition: For a function $y=h(x)$ with domain $M$, the equation of the tangent line at point $(x_{0},f(x_{0}))$ is $l$: $y=g(x)$. If $\frac {h(x)-g(x)}{x-x_{0}} > 0$ always holds within $M$, then $P$ is called a "pseudo-symmetry point" of the function $y=h(x)$. Question: Does the function $y=f(x)$ have any "pseudo-symmetry points"? If yes, please find at least one "pseudo-symmetry point"; if no, please explain why.

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