
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
Calculate the area of the closed shape formed by the graph of the function $f(x) = \begin{cases} x^{2} & (0 \leq x \leq 1) \\ 2-x & (1 < x \leq 2)\end{cases}$ and the x-axis.

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