
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 cube consists of eight identical smaller cubes. Three of the small cubes are replaced by ones of the same size but with three times the density. Determine the ratio of the final density to the initial density of the larger cube.

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