
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 marathons, Chinese athlete He Jie won the men's event in 2 hours, 13 minutes, and 2 seconds, securing China's first-ever men's marathon gold medal in the Asian Games. Human long-distance running is generally divided into two stages: the first stage is a stable phase lasting for the first hour, and the second stage is a fatigue phase. Suppose a 60kg rehabilitation marathon athlete undergoes a 4-hour long-distance running training session. In the stable phase, the athlete runs at a speed of $v_{1}=30km/h$ and expends energy $\Delta Q_{1}=t_{1}\times 2v_{1}$ per kilogram of body weight (where $t_{1}$ represents the time spent in this phase). In the fatigue phase, due to excessive energy consumption, the speed decreases to $v_{2}=30-10t_{2}$ (where $t_{2}$ represents the time spent in this phase). In this phase, with a certain recovery of energy, the athlete expends energy $\Delta Q_{2}=\frac{t_{2}×2v_{2}}{t_{2}+1}$ per kilogram of body weight. Given that the initial energy of the athlete is $Q_{0}=10000kJ$, without considering other factors, and the time spent is $t$ (unit: hours), please answer the following questions:  
$(1)$ Write down the function $Q(t)$ representing the remaining energy of the athlete as a function of time $t$.  
$(2)$ At what time within the 4-hour period does the athlete's energy reach its lowest point? What is the value of the lowest energy level?

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