
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
Let the temperature $T$ of an object during a day be a function of time $t$: $T(t)=a t^{3}+b t^{2}+c t+d(a \neq 0)$, where the temperature is in degrees Celsius (${}^{\circ} \mathrm{C}$) and time is in hours, with $t=0$ representing 12:00 PM and positive $t$ representing times after 12:00 PM. If the temperature of the object at 8:00 AM is $8^{\circ} \mathrm{C}$, at 12:00 PM is $60^{\circ} \mathrm{C}$, and at 1:00 PM is $58^{\circ} \mathrm{C}$, and it is known that the rate of change of temperature is the same at 8:00 AM and 4:00 PM:
1. Write the function $T$ expressing the temperature $T$ in terms of time $t$;
2. Determine at what time between 10:00 AM and 2:00 PM (inclusive) the temperature is highest, and find the highest temperature.

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