
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
**Background:** Define a new operation "$*$": the result of the operation takes the positive sign if the signs are the same, and negative if the signs are different. The value is the sum of their absolute values. When $0$ is operated with any number using "$*$", the result is the absolute value of that number. For example:  
$(+2)*\left(+3\right)=5,\left(-2\right)*\left(-3\right)=5$;  
$(-2)*\left(+3\right)=-5,\left(+2\right)*\left(-3\right)=-5$;  
$0*\left(+2\right)=2$,$\left(-2\right)*0=2$;  
$\ldots$

**Rephrased Problem:**  
(1) Calculate: $\left(-15\right)*\left[\left(+3\right)*0\right]$;  
(2) Calculate: $\left[\left(+3\right)*a\right]+a$.

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