
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 $f(x)=-f'(0)e^{x}+2x+3$, line $l$ is the tangent line of the curve $y=f(x)$ at the point $(0,f(0))$. Point $P$ is on line $l$, and point $Q$ is on the curve $y=\frac{x}{e^{x}}$. The minimum value of $|PQ|$ is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$

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