
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
Use the fundamental theorem of calculus or the geometric meaning of definite integrals to find the definite integrals of the following functions:
\[(1)\int_{0}^{1}(x^{2}{-}x){dx}\quad(2)\int_{1}^{3}{{|}}x{-}2{|}{dx}\quad(3)\int_{0}^{1}\sqrt{1{-}x^{2}}{dx}\]

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