
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
Two ships depart from the same port in opposite directions, with ship A going downstream and ship B going upstream. The speed of the water flow is $a$ km/h.  
$(1)$ If the speed of both ships in still water is $50$ km/h, find how many kilometers ship A travels more than ship B after $2$ hours.  
$(2)$ A small speedboat shuttles tourists between docks A and B. The time taken for the outbound trip is three times the time taken for the return trip. Find the relationship between the speed $m$ of the speedboat in still water and the speed $a$ of the water flow.

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