
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 $f(x) = xe^x$ and $g(x) = -(x+1)^2 + a$, if there exist $x_1, x_2 \in [-2, 0]$ such that $f(x_2) \leq g(x_1)$, then determine the range of values for the real number $a$.

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