
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/>$(1)a^{4}\cdot (a^{2})^{3}$;<br/>$(2)2a^{3}b^{2}c\div (\frac{1}{3}a^{2}b)$;<br/>$(3)6a(\frac{1}{3}ab-b)-\left(2ab+b\right)\left(a-1\right)$;<br/>$(4)\left(a-2\right)^{2}-\left(3a+2b\right)\left(3a-2b\right)$.

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