
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. Two of the small cubes were replaced with cubes of the same size but twice the density. Determine the ratio of the initial to the final density of the large cube.

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