
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
Water is cooled by placing it in air with a temperature of $θ_{0}℃$. If the original temperature of the water is $θ_{1}℃ (θ_{0} < θ_{1})$, the temperature of the object $θ℃$ after $t$ minutes can be obtained by the formula $θ=θ_{0}+(θ_{1}-θ_{0})e^{-kt}$, where $k$ is a positive constant determined by different containers holding the water.

(1) If the room temperature is $20℃$, hot water at $98℃$ is poured into a certain container. After one hour, the water temperature is measured to be $71.2℃$. Find the value of $k$ (accurate to 0.001).

(2) If the $k$ value of a thermos is 0.01, boiling water at $100℃$ is poured into the thermos. After 2.5 hours, the water temperature is measured to be $40℃$. Find the room temperature at this time (assuming the room temperature is constant, accurate to $0.1℃$).

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