
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 this year's "May Day Golden Week," tourism along the Three Gorges of the Yangtze River once again became popular nationwide, with the Zhong County Shibaozhai Scenic Area attracting large crowds. The "Alliance Luxury Tourist Liner" travels at a constant speed between Chongqing and Shibaozhai, which are about 270 kilometers apart. It takes 9 hours to travel downstream from Chongqing to Shibaozhai, and it takes 4.5 hours longer to travel upstream from Shibaozhai to Chongqing.

$(1)$ Find the speed of the liner in still water and the speed of the water flow.

$(2)$ If a new dock needs to be built between Chongqing Port and Shibaozhai to allow tourists to rest and sightsee, and the liner takes the same amount of time to travel from Chongqing Port to the new dock as it does from Shibaozhai to the new dock, how far apart are Chongqing Port and the new dock in kilometers?

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