
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
Define the ☆ operation: observe the following expressions:  
$1$☆$2=1\times 3+2=5$;  
$4$☆$(-1)=4\times 3-1=11$;  
$(-5)$☆$3=(-5)\times 3+3=-12$;  
$(-6)$☆$(-3)=(-6)\times 3-3=-21\ldots$  
$(1)-1$☆$2=$______, $a$☆$b=$______;  
$(2)$ If $a \lt b$, then $a$☆$b-b$☆$a$ ______ 0 (use "$ \gt $", "$ \lt $", or "$=$ to connect");  
$(3)$ If $a$☆$(-2b)=4$, please calculate the value of $\left[3\left(a-b\right)\right]$☆$\left(3a+b\right)$.

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