
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
甲、乙两名魔方爱好者在$30$秒内复原魔方的概率分别是$0.8$和$0.6$.如果在$30$秒内将魔方复原称为"复原成功",且每次复原成功与否相互之间没有影响,求:（1）甲复原三次,第三次才成功的概率；（2）甲、乙两人在第一次复原中至少有一人成功的概率.

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