
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 or factorize:

1. Calculate: $\sqrt [3] {27}+\sqrt {\dfrac{1}{9}}\div \left(-\dfrac{2}{3}\right)+|-\dfrac{1}{2}|$;
2. Factorize: $(x-2)(x-4)+1$;
3. Calculate: $\left(2x^{2}y\right)^{3}\cdot 5xy^{2}\div \left(-10x^{6}y^{5}\right)+\left(x^{2}y-2xy\right)\div xy$.

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