
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 $f(x) = (x+1)^2e^x$, and let $k \in [-3, -1]$. For any $x_1, x_2 \in [k, k+2]$, calculate the maximum value of $|f(x_1) - f(x_2)|$.

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