
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
During the National Day holiday, Xiao Li drove his car from home to Yinping Mountain for a trip. According to the navigation, he can reach Yinping Mountain by driving at a speed of $80 km/h$ for $3h$. If the car travels at a constant speed of $v km/h$ for a time of $t h$,

$(1)$ Find the function expression of $v$ in terms of $t$;

$(2)$ If on the return trip, the car travels at a constant speed of $60 km/h$, assuming the road conditions and other factors are the same as when he went, how many hours will it take for him to return from Yinping Mountain to home?

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