
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
We have brick pieces with dimensions $22 \mathrm{~cm}$ in length, $11 \mathrm{~cm}$ in width, and $6 \mathrm{~cm}$ in height. These bricks need to fill a rectangular parallelepiped - $ABCDEFGH$ - in such a way that the $22 \mathrm{~cm}$ edges are parallel to the length $AB$ of the pile, the $11 \mathrm{~cm}$ edges are parallel to the width $BF$ of the pile, and the $6 \mathrm{~cm}$ edges are parallel to the height $AD$ of the pile. The length $AB$ is $1 \frac{1}{4}$ times the height $AD$, and the width $BF$ is $1 \frac{1}{2}$ times the height $AD$. What is the minimum number of brick pieces needed to satisfy the given requirement?

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