
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
The track and field events of the Hangzhou Asian Games concluded on October 5th. In the final two events, the men's and women's marathon races, Chinese athlete He Jie won the men's group championship with a time of 2 hours, 13 minutes, and 2 seconds, marking the first men's marathon gold medal in the history of the Asian Games for China. Human long-distance running is generally divided into two stages: the first stage is a stable stage lasting for the first hour, and the second stage is a fatigue stage. Now, a 60kg rehabilitation marathon athlete is undergoing a 4-hour long-distance running training. Assuming that the athlete's stable stage runs at a speed of $v_{1}=30km/h$ at a constant speed, the energy consumption per kilogram of body weight in this stage is $\Delta Q_{1}=t_{1}\times 2v_{1}$ (where $t_{1}$ represents the time spent in this stage). In the fatigue stage, due to excessive energy consumption, the speed decreases to $v_{2}=30-10t_{2}$ for decelerated motion (where $t_{2}$ represents the time spent in this stage). With the speed decrease in the fatigue stage, the energy consumption per kilogram of body weight is $\Delta Q_{2}=\frac{{t}_{2}×2{v}_{2}}{{t}_{2}+1}$. Given that the initial energy of the athlete is $Q_{0}=10000kJ$, without considering other factors, and the time taken is $t$ (unit: $h$), please answer the following questions:  
$(1)$ Write down the function $Q(t)$ representing the remaining energy of the athlete as a function of time $t$.  
$(2)$ When does the athlete reach the lowest energy level within the 4-hour period? What is the value of the lowest energy level?

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