
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
Let $n = \overline {ab}$ represent a two-digit number, and define the function $f(n) = a + b + a \times b$. For example, $f(12) = 1 + 2 + 1 \times 2 = 5$. Find the number of two-digit integers such that $f(n) = n$.

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