
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
Let the function $y=f\left(x\right)$ have domain $D$, and all points on its graph be above the line $y=t$. If the function $f\left(x\right)=\left(x-t\right)e^{x}$ has the domain $R$ and is a "$\left(-\infty ,+\infty \right)-t$ function", determine the largest integer value of the real number $t$.

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