
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 $f(x)=(x+1)e^{-x}$ (where $e$ is the base of the natural logarithm),
- (I) Find the intervals of monotonicity for the function $f(x)$;
- (II) Let the function $\varphi(x)=xf(x)+tf'(x)+e^{-x}$. If there exist ${x}_1,{x}_2 \in [0,1]$ such that $2\varphi({x}_1) < \varphi({x}_2)$ holds, find the range of the real number $t$.

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