
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
Each of the integers 1 to 7 is to be written, one in each circle in the diagram, and the sum of the three integers in any straight line is to be the same. Calculate the number of different ways the centre circle can be filled.

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