
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 metal sphere, which initially had a temperature of $12^{\circ} \mathrm{C}$, is being cooled by a stream of water at $0^{\circ} \mathrm{C}$. After 8 minutes, the sphere's temperature drops to $9^{\circ} \mathrm{C}$. Assuming that the cooling rate is proportional to the difference between the temperature of the sphere and the temperature of the cooling medium, determine the time it takes for the sphere to cool down to $7^{\circ} \mathrm{C}$.

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