
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
Arrange the natural numbers from 1 to 16 into a $4 \times 4$ matrix such that the sum of numbers in each row, each column, and each diagonal is 34. Such a matrix is called a 4th-order magic square, and 34 is called the magic constant of the 4th-order magic square. The Southern Song Dynasty mathematician Yang Hui, who was the earliest to systematically study magic squares, named them "vertical and horizontal diagrams." Not only did he provide the following two beautiful 4th-order magic squares, but he also studied 10th-order magic squares. The magic constant of the 10th-order magic square is $\qquad$.

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