
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
$$ f(x) = \begin{cases} x^2, & x \in [0,1) \\
2 - x, & x \in [1,2] \end{cases}, $$
calculate the integral
$$ \int_{0}^{2} f(x)dx. $$

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