
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
The density of a body $\rho$ is defined as the ratio of the mass $m$ to its volume $V$. In the jewelry industry, the unit of mass is the carat (1 carat equals 0.2 grams). In many countries, the unit of length is the inch (1 inch equals 2.54 centimeters). It is known that the density of emerald is $\rho = 2.7 \text{ g/cm}^3$. Convert this value to carats per cubic inch.

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