
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
The equation \( x^2 - (1B)x + B1 = 0 \) has positive integer solutions where \( B \) is a positive single digit. How many such \( B \)s exist? (Since \( B \) represents a digit, if \( B = 3 \) then \( B1 \) represents the integer 31.)

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