
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
Material question: Please read the following information carefully and try to give your answer and solution. There are three sets of numbers here:  
①$3$,$6$,$9$,$12$;  
②$0$,$-2$,$-4$,$-6$,$-8$;  
③$8$,$5$,$2$,$\ldots \ldots $  
Sets ① and ② consist of a finite number of elements, while set ③ consists of an infinite number of elements. They all have in common: they are arranged in a certain order to form a sequence of numbers, called a sequence. Each number in the sequence is called a term of the sequence, and each term is called the first term (or initial term), the second term, the third term, $\ldots$, the $n$th term, $\ldots$ generally denoted as $a_{1}$, $a_{2}$, $a_{3}\ldots \ldots $ These three sets of sequences all start from the second term, and each term starting from the second term has the same constant difference with its preceding term, then this sequence is called an arithmetic sequence. This constant is called the common difference, and the common difference is usually represented by the letter $d$.  
Question (1): If in sequence ① $d=3$ and in sequence ② $d=-2$, then in sequence ③ $d=\_\_\_\_\_\_$.  
Also, as $a_{2}=a_{1}+d$,  
$a_{3}=a_{2}+d=(a_{1}+d)+d=a_{1}+2d$,  
Question (2): $a_{4}=a_{3}+d=(a_{1}+2d)+d=a_{1}+$______.  
$\ldots \ldots $  
(3) From this, we can obtain $a_{n}=a_{1}+\_\_\_\_\_\_d$  
(4) Based on the conclusion of (3), can you find the $4$th and $15$th terms of the arithmetic sequence $3$,$7$,$11$,$\ldots$?

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