
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
Let  $g(t)$  be the minimum value of  $f(x)=x2^{-x}$  in  $t\leq x\leq t+1$ .
Evaluate  $\int_0^2 g(t)dt$ .

*2010 Kumamoto University entrance exam/Science*

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