
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 following definite integrals.  
(1) $\int_{-3}^{2} |x+1| \, dx$  
(2) Let $f(x)= \begin{cases} x^{2} & (0\leqslant x < 1)\\ 2-x & (1\leqslant x\leqslant 2) \end{cases}$, then calculate $\int_{0}^{2} f(x) \, dx$.

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