
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
If a two-digit number $N$ satisfies $N=ab+a+b$, where $a$ and $b$ are positive integers, then $N$ is called a good number. The largest good number is ______; if $a$ and $b$ also satisfy $\frac{ab}{a+b}=3$ or $4$, then $N$ is called an absolute good number. The number of absolute good numbers is ______.

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