
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) $\int_{0}^{1} (2x - x^2)dx$;

(2) $\int_{2}^{4} (3 - 2x)dx$;

(3) $\int_{0}^{1} \frac{1}{3}x^2 dx$;

(4) $\int_{0}^{2π} \cos x dx$.

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