
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 $f(x)= \begin{cases} x^{2}, x \in [0,1], \\ 2-x, x \in (1,2], \end{cases}$ find the value of $\int_{0}^{2}f(x)dx$. The possible answers are:
A) $\dfrac{3}{4}$
B) $\dfrac{4}{5}$
C) $\dfrac{5}{6}$
D) Does not exist

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