
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
Simplify first and then evaluate: $[\left(3a+2b\right)\left(3a-2b\right)+\left(3a-b\right)^{2}-b\left(2a-3b\right)]\div 2a$, where $a$ and $b$ satisfy $|a-1|+b^{2}-6b+9=0$.

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