
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. On the surface, there is floating freshwater ice with a mass of $m=100$ g. 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 $\rho_{\mathrm{n}}=0.9$ g/cm³, the density of saltwater is $\rho_{\mathrm{св}}=1.03$ g/cm³, and the density of freshwater is $\rho_{\text{пв}}=1$ g/cm³. Ignore the change in total volume when mixing two liquids.

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