
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 left diagram below, seven letters are placed in a circle. Each time, three circles that include the center circle (with the centers forming an equilateral triangle) are rotated $120^{\circ}$ clockwise. This is called an operation. For example, we can rotate $A, B, D$ such that $B$ appears in the position of the original $D$ (denoted as $B \rightarrow D$), $D \rightarrow A$, and $A \rightarrow B$. We can also rotate $D, E, F$ ($D \rightarrow E$, $E \rightarrow F$, $F \rightarrow D$), but we cannot rotate $A, D, G$ or $C, B, E$. After a number of operations, we obtain the right diagram. What is the minimum number of operations needed?

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