
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
Assuming a three-digit number $n = \overline {abc}$ (meaning $n=100a+10b+c$, where $a, b, c \in \mathbb{N}^*$), if $a$, $b$, $c$ can be the lengths of the three sides of an isosceles (including equilateral) triangle, determine the number of such three-digit numbers $n$.

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