
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 high jumper has a probability of $p=0.8$ to clear 1.8m. Assuming each jump does not deplete his energy, calculate:  
(1) The probability that he successfully clears the height on two consecutive jumps.  
(2) The probability that he clears the height for the first time on his third attempt.  
(3) The minimum number of attempts required to clear 1.8m with a 99% probability.  
(Note: You may need the value $\log_{10}2=0.3010$)

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