
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 $f(x)=(x^{2}+2x+1)e^{x}$, let $t\in\[-3,-1\]$, for any $x\_{1}$, $x\_{2}\in\[t,t+2\]$, the maximum value of $|f(x\_{1})-f(x\_{2})|$ is $\_\_\_\_\_\_\_\_\_\_\_\_$.

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