
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
Find how many two-digit positive integers can be expressed as the sum of the non-zero tens digit, the twice of the units digit, and the product of the tens and units digits, i.e., the number \(10a + b\) satisfies the equation \(10a + b = a + 2b + ab\) where \(a\) and \(b\) are the tens and units digits, respectively.

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