
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 $a*b=ab+a+b$, for example, $1*2=1\times 2+1+2=5$, $1*a=1\times a+1+a=2a+1$. For the operation "$*$", the following equations hold true: ① $a*b=b*a$; ② $\left(a+1\right)*b=a*b+1*b$; ③ $\left(a*b\right)*c=a*\left(b*c\right)$.

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