
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 $f(x)=a(e^{x}-x)-e^{-x}-x$ where $a\in \mathbb{R}$.  
$(1)$ If $a=e$, find the monotonic intervals of the function $f(x)$.  
$(2)$ When $0 < a < 1$, let $x_{1}$ and $x_{2}$ be the points where $f(x)$ has a local maximum and local minimum respectively, and $f(x_{1})+tf(x_{2}) > 0$. Find the range of values for $t$.

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