
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 $g(x)=\frac{1}{e^{x}}$, determine the range of values for the real number $a$ such that there exist $x_1\in[\frac{1}{2},2]$ and $x_2\in[\frac{1}{2},2]$ such that $f'(x_1)\leqslant g(x_2)$ holds true.

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