
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
There are three different sizes of cubic blocks, labeled as A, B, and C. The edge length of block A is $\frac{1}{2}$ the edge length of block B, and the edge length of block B is $\frac{2}{3}$ the edge length of block C. If these blocks are to be used to form a larger cube with the smallest possible volume (using at least one of each type), how many of these blocks are needed in total?

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