
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

In winter, at an ambient air temperature of \(t_{0} = -20^{\circ} \mathrm{C}\), each square meter of a lake transfers 300 kJ of heat per hour to the air. Estimate how long after the formation of ice a fisherman can safely venture onto the lake if the safe ice thickness is 10 cm. The water temperature \(t_{\mathrm{B}} = 0^{\circ} \mathrm{C}\). The latent heat of fusion of ice is 330 kJ/kg, its specific heat capacity is 2100 J/kg \({ }^{\circ} \mathrm{C}\), and the density of ice is 900 kg/m\(^3\). Assume the heat transfer rate is constant.

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