
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/>$(1){(-3)}^{2}-|-\frac{1}{2}|+{2}^{-1}-{(π-3.14)}^{0}$;<br/>$(2)a^{5}\cdot \left(-a\right)^{3}+(-2a^{2})^{4}$;<br/>$(3)({2a}^{2}-{2b}^{2})(-\frac{1}{2}ab)$;<br/>$(4)\left(a+b\right)\left(a-2b\right)$.

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