
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, cycling is very popular among citizens. Two cycling enthusiasts, A and B, agreed to ride along the same route from point $A$ to point $B$, which is 30 kilometers away from point $A$. It is known that A rides at a speed 1.2 times faster than B.<br/>$(1)$ If B rides 2 kilometers first and A starts from point $A$ only when B starts, then A catches up with B exactly half an hour later. Find the speed of A.<br/>$(2)$ If B rides for 20 minutes first and A starts from point $A$ only when B starts, then A and B arrive at point $B$ at the same time. Find the speed of A.

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