
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 $f(x)=\frac{x+1}{e^{x}}$,
(I) Find the maximum value of the function $f(x)$;
(II) Suppose the maximum value of the function $g(x)=xf(x)+tf′(x)+e^{-x}\ (t∈R)$ defined on $[0,1]$ is $M$, and the minimum value is $N$. If $M > 2N$, find the range of the real number $t$.

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