
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
(1) Please fill in an appropriate algebraic expression in the blank spaces in the table below: In a staircase classroom of a certain school, the number of seats in the 1st row is 12. Starting from the 2nd row, each row increases by $a$ seats. 

| Row Number | 1st Row | 2nd Row | 3rd Row | 4th Row | $\cdots$ | $n$th Row |
|------------|---------|---------|---------|---------|----------|-----------|
| Number of Seats | 12 | $12+a$ | ______ | ______ | $\cdots$ | ______ |

(2) Given that the number of seats in the 15th row is twice the number of seats in the 5th row, find the value of $a$.

(3) Under the condition in (2), calculate how many seats are there in the 21st row?

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