
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 $f(x)=\frac{1}{3}x^3+x^2+ax$. If $g(x)=\frac{1}{e^x}$, there exist $x\_1 \in [\frac{1}{2},2]$ and $x\_2 \in [\frac{1}{2},2]$ such that the derivative of function $f(x)$, denoted as $f'(x\_1)$, satisfies $f'(x\_1) \leq g(x\_2)$. Determine the range of values for the real number $a$.

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