
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 salt water. A piece of fresh ice with a mass of $m=50$ g floats on the surface. What is the volume $\Delta V$ of water that will overflow from the glass by the time the ice melts? Neglect surface tension. The density of fresh ice is $\rho_{\mathrm{n}}=0.9 \,\text{g/cm}^3$, the density of salt ice is $\rho_{\mathrm{c}}=0.95 \,\text{g/cm}^3$, the density of fresh water is $\rho_{\text{fw}}=1 \,\text{g/cm}^3$, and the density of salt water is $\rho_{\mathrm{sw}}=1.03 \,\text{g/cm}^3$. Neglect the change in total volume when mixing the two liquids.

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