
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 $$f(x)= \frac {1}{3}x^{3}+mx^{2}+nx+2$$, its derivative $f′(x)$ is an even function, and $f(1)=- \frac {2}{3}$. Find the minimum value of the function $g(x)=f′(x)e^x$ on the interval $[0,2]$.

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