
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
The shape of a game board is a rhombus with a $60^{\circ}$ angle. Each side of the rhombus is divided into 9 equal parts, and through each dividing point, two lines are drawn parallel to the sides and the shorter diagonal, respectively, dividing the rhombus into many small equilateral triangles. If a game piece is placed on the center of one of these small triangles, three lines are drawn through this center parallel to the three sides of the triangle, and all the small triangles that these lines pass through are considered controlled by this piece. What is the minimum number of pieces needed to control all the small triangles on the game board?

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