
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. Solve the inequality $f(x) \leq 0$ when $a=\frac{1}{2}$;
2. Compare the values of $a$ and $\frac{1}{a}$;
3. Solve the inequality $f(x) \leq 0$ with respect to $x$.

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