
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
Find the maximum value of the function $y=\frac{x}{{{e}^{x}}}$ on the interval $[0,2]$.

A) When $x=1$, $y=\frac{1}{e}$
B) When $x=2$, $y=\frac{2}{{{e}^{2}}}$
C) When $x=0$, $y=0$
D) When $x=\frac{1}{2}$, $y=\frac{1}{2\sqrt{e}}$

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