
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
Given the temperature cooling model $t=-\frac{1}{k}\ln\frac{{\theta-\theta_{0}}}{{\theta_{1}-\theta_{0}}}$, assuming a cup of boiling water has an initial temperature of $\theta_{1}=100^{\circ}C$, an ambient temperature of $\theta_{0}=20^{\circ}C$, and a constant $k=0.2$, find the approximate time in minutes required for the water temperature to drop to $40^{\circ}C$.

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