
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 $f(x)=x^{2}-\left( \frac {a+1}{a}\right)x+1$, where $a > 0$  
$(1)$ When $a= \frac {1}{2}$, solve the inequality $f(x)\leqslant 0$;  
$(2)$ Compare the size of $a$ and $\frac {1}{a}$;  
$(3)$ Solve the inequality $f(x)\leqslant 0$ with respect to $x$.

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