
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 $f(x) = \frac{1}{3}x^3 + x^2 + ax$, and $g(x) = \frac{1}{e^x}$, for any $x_1 \in \left[\frac{1}{2}, 2\right]$, there exists $x_2 \in \left[\frac{1}{2}, 2\right]$ such that $f'(x_1) > g(x_2)$ holds. Find the range of the real number $a$.

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