
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
According to the latest revision of the "Regulations on the Application and Use of Motor Vehicle Driving Licenses" by the Ministry of Public Security: each driving license applicant must pass the "Subject One" (theoretical subject) and "Comprehensive Subject" (combination of driving skills and some theoretical knowledge of "Subject One") exams. It is known that Mr. Li has passed the "Subject One" exam, and the score of "Subject One" is not affected by the "Comprehensive Subject". The "Comprehensive Subject" offers 5 chances to take the exam within three years. Once an exam is passed, the driving license will be issued, and the applicant will no longer participate in subsequent exams; otherwise, the exams will continue until the 5th attempt. The probabilities of Mr. Li passing the "Comprehensive Subject" in each attempt are 0.5, 0.6, 0.7, 0.8, and 0.9, respectively.
(1) Calculate the distribution and mathematical expectation of the number of times ξ that Mr. Li takes the driving license test within three years.
(2) Calculate the probability of Mr. Li obtaining a driving license within three years.

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