
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

An aluminum cube with an edge length of \( l = 10 \) cm is heated to a temperature of \( t_{1} = 100^{\circ} \mathrm{C} \). After this, it is placed on ice, which has a temperature of \( t_{2} = 0^{\circ} \mathrm{C} \). Determine the maximum depth to which the cube can sink. The specific heat capacity of aluminum is \( c_{a} = 900 \) J/kg\(^\circ \mathrm{C} \), the specific latent heat of fusion of ice is \( \lambda = 3.3 \times 10^{5} \) J/kg, the density of aluminum is \( \rho_{a} = 2700 \) kg/m\(^3 \), and the density of ice is \( \rho_{n} = 900 \) kg/m\(^3 \).

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