
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 $f(x)=\dfrac{ax^{2}+x+a}{2e^{x}}$.

(I) If $a\geqslant 0$, the maximum value of the function $f(x)$ is $\dfrac{5}{2e}$, find the value of the real number $a$;

(II) If for any $a\leqslant 0$, $f(x)\leqslant \dfrac{b\ln(x+1)}{2}$ holds true for $x\in [0,+\infty)$, find the range of the real number $b$.

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