
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 three-digit number is called a "harmonious number" if its tens digit is equal to the sum of its units digit and hundreds digit.  
$(1)$ The smallest three-digit "harmonious number" is ______, and the largest three-digit "harmonious number" is ______;  
$(2)$ If the units digit of a "harmonious number" is $a$ ($a\geqslant 0$), and the tens digit is $b$ ($b\geqslant 1$, $b>a$, and both $a$ and $b$ are natural numbers), express this "harmonious number" using an algebraic expression containing $a$ and $b$.

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