
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 square-based pyramid arrangement of blocks with 30 blocks, arranged such that the bottom layer forms a square of 16 blocks, the next layer forms a square of 9 blocks, then a 4 block square, topped by one block. Each block in the upper layer is assigned a number which is the average (mean) of numbers assigned to the four blocks directly below it (or nearest in arrangement). The blocks in the bottom layer are numbered from 1 through 16, in some suitable sequence. Determine the smallest possible number which could be assigned to the top block.

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