
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 certain type of lottery ticket consists of a 7-digit number, with each digit being any one of the 10 digits from 0 to 9. A 7-digit number (the first digit can be 0) is drawn as the winning number. If the 7 digits of a lottery ticket match the winning number, it wins the first prize. If any 6 consecutive digits match the corresponding digits of the winning number, it wins the second prize. If any 5 consecutive digits match the corresponding digits of the winning number, it wins the third prize. No ticket can win more than one prize. Suppose someone bought a lottery ticket and assume the winning number for this lottery is 1234567.  
(1) Calculate the probability of winning the second prize;  
(2) Calculate the probability of winning the third prize or higher.

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