
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
In the 6 circles below, fill in the numbers $1, 2, 3, 4, 5, 6$, each number used exactly once, such that the sum of the three numbers on each side is equal. This sum is called the "magic sum" for the sides of the triangle. What possible values can this magic sum take?

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