
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
$(1)$ Simplify the calculation: $6.9^{2}+6.2\times 6.9+3.1^{2}$;<br/>$(2)$ Simplify and find the value of: $(a^{2}b^{3}+2a^{3}b)\div \left(2ab\right)-\left(a+2b\right)\left(a-2b\right)$, where $a=1$, $b=\frac{1}{2}$.

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