
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
Place water in air at a temperature of $\theta$℃ to cool it. If the original temperature of the water is $\theta_1$℃ ($\theta < \theta_1$), the temperature $\theta$℃ of the object after $t$ minutes can be obtained by the formula $\theta = \theta + (\theta_1 - \theta)e^{-kt}$, where $k$ is a positive constant determined by the different containers holding the water.  
(1) If the room temperature is 20℃, and hot water at 98℃ is poured into a container, and the water temperature is measured to be 71.2℃ after one hour, find the value of $k$; (accurate to 0.001)  
(2) If the $k$ value for a thermos is 0.01, and boiling water at 100℃ is poured into the thermos, and the water temperature is measured to be 40℃ after 2.5 hours, find the room temperature at that time (assuming the room temperature is constant, accurate to 0.1℃).

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