
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/>$(1)(a^{2}b)^{2}\div (a^{2}b^{2})$;<br/>$ \left(2\right)99\times 101+1$ (calculate using multiplication formula);<br/>$(3)x^{2}y(x^{2}+2y)-2x^{2}y^{2}$;<br/>$(4)$ Simplify and find the value of $\left(x+2y\right)^{2}+\left(x+2y\right)\left(x-2y\right)-4xy$, where $x=1$ and $y=2^{100}$.

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