
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:<br/>$(1)2mn^{2}\cdot \frac{1}{4}mn$;<br/>$(2)(2a^{3}b^{2}+a^{2}b)\div ab$;<br/>$(3)\left(2x+3\right)\left(x-1\right)$;<br/>$(4)\left(x+y\right)^{2}-2y\left(x-y\right)$.

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