
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
Consider a new arrangement of cubical blocks where:
- The base layer has 12 blocks arranged in a rectangular pattern (4 blocks by 3 blocks). 
- A second layer of 6 blocks rests on the base layer arranged such that each block sits on 2 base layer blocks (think staggered rows).
- A third layer of 2 blocks is placed each on three of the second layer blocks.
- A single top block rests on the two third-layer blocks.
The blocks in the base layer are numbered from 1 to 12 in some order. Each block in subsequent layers gets a number that is the sum of the numbers of the blocks directly beneath it. Given that arrangement, find the smallest possible number that could be assigned to the top block.
A) 72
B) 89
C) 95
D) 104

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