
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 distance from the Xinzhou Government Office Building to Huaihua High-Speed Railway Station is approximately $90$ kilometers. Xiao Huang drives a sedan, and Lao Zhang takes a bus, both heading from the Xinzhou Government Office to Huaihua High-Speed Railway Station. Xiao Huang departs $20$ minutes later than Lao Zhang, but they arrive at Huaihua High-Speed Railway Station at the same time. It is known that the speed of the sedan is $1.5$ times that of the bus.
$(1)$ What are the speeds of the sedan and the bus? (Solve by setting up equations)
$(2)$ How far is Lao Zhang from Huaihua High-Speed Railway Station when Xiao Huang departs?

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