
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:<br/>$(1)a^{3}\cdot a+(2a^{2})^{2}$;<br/>$(2)a^{4}+(-2a^{2})^{3}-a^{8}\div a^{4}$;<br/>$(3)\left(a+1\right)\left(a-1\right)-a\left(a-3\right)$;<br/>$(4)\left(a+1\right)^{2}+\left(a+1\right)\left(a-2\right)$.

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