
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 that the temperature \( T \) of an object throughout the day is a function of time \( t \): \( T(t) = a t^3 + b t^2 + c t + d \) (\(a \neq 0\)). The temperature is measured in \(^\circ \text{C}\), and time is measured in hours. Here, \( t = 0 \) represents 12:00 PM, and positive values of \( t \) represent times after 12:00 PM. The following temperatures are observed:
- At 8:00 AM (\( t = -4 \)): \( T = 8^\circ \text{C} \)
- At 12:00 PM (\( t = 0 \)): \( T = 60^\circ \text{C} \)
- At 1:00 PM (\( t = 1 \)): \( T = 58^\circ \text{C} \)

Additionally, the rate of temperature change at 8:00 AM and 4:00 PM is the same.

(1) Write the function \( T \) in terms of \( t \).

(2) During the period between 10:00 AM and 2:00 PM (including 10:00 AM and 2:00 PM), at what time is the temperature highest? Also, determine the highest temperature.

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