
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
Fill the circles with natural numbers from 1 to 12 (each number used exactly once), so that the sum of the numbers in any four circles on the same straight line is equal. This arrangement is called a 6th-order magic star, and the corresponding sum is called the magic sum of the 6th-order magic star. What is the magic sum of the 6th-order magic star? Additionally, complete the following 6th-order magic star diagram.

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