
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
In the national fitness movement, running is quite popular among citizens. Runners A and B agreed to run from point $A$ along the same route to point $B$, which is 8 kilometers away from point $A$. It is known that the speed of runner A is 1.2 times that of runner B.  
$(1)$ If runner B runs 1 kilometer first and then runner A starts from point $A$, runner A catches up with runner B exactly half an hour later. Find the speed of runner A.  
$(2)$ If runner B runs for 10 minutes first and then runner A starts from point $A$, runner A and runner B arrive at point $B at the same time. Find the speed of runner A.

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