
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 seven-digit number \( a \), with the sum of its digits being \( b \), is given. It is known that \( a - b \) is still a seven-digit number, and six of the digits of \( a - b \) are 1, 2, 3, 4, 6, and 7. If Xiaoming is smart enough, what is the probability that he can correctly guess the seventh digit?

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