
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 $f(x)=\frac{x}{{e}^{x}}$ for $x>0$.
1. Find the maximum value of the function $f(x)$.
2. If the function $g(x)=f(x)-m$ has two zeros, find the range of real number $m$.
3. If the inequality $f^2(x)-af(x)>0$ has only one integer solution, find the range of real number $a$.

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