
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
Regular hexagon \(ABCDEF\) has its center at \(G\). Each of the vertices and the center are to be associated with one of the digits \(1\) through \(7\), with each digit used once, in such a way that the sums of the numbers on the lines \(AGC\), \(BGD\), and \(CGE\) are all equal. How many ways can this be done?

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