
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
A certain boat travels downstream for $3$ hours and upstream for $1.5$ hours. It is known that the speed of the boat in still water is $akm/h$, and the speed of the water flow is $ykm/h$. Answer the following questions:
- $(1)$ The speed and distance of the boat traveling downstream.
- $(2)$ The speed and distance of the boat traveling upstream.
- $(3)$ How far did the boat travel in total?

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