
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 glass is filled to the brim with saltwater. A piece of freshwater ice with a mass of $m=100$ grams is floating on the surface. What volume $\Delta V$ of water will spill out of the glass by the time the ice melts? Neglect surface tension. The density of freshwater ice is $\rho_{n}=0.92 \, \text{g/cm}^3$ and the density of saltwater is $\rho_c = 0.952 \, \text{g/cm}^3$, the density of freshwater is $\rho_{n \in}=1 \, \text{g/cm}^3$. Neglect the change in total volume when mixing two liquids.

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