
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

A game board is in the shape of a rhombus with an angle of $60^\circ$. Each side of the rhombus is divided into nine parts. Lines are drawn through the division points, parallel to the sides and the shorter diagonal of the rhombus, dividing the board into triangular cells. If a piece is placed on a cell, three lines are drawn through it, parallel to the sides and the shorter diagonal of the rhombus. The cells these lines intersect will be considered captured by the piece. What is the minimum number of pieces needed to capture all the cells on the board?

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