
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  $N=\overline{abc}$  be a three-digit number. It is known that we can construct an isoceles triangle with  $a,b$  and  $c$  as the length of sides. Determine how many possible three-digit number  $N$  there are.

( $N=\overline{abc}$  means that  $a,b$  and  $c$  are digits of  $N$ , and not  $N=a\times b\times c$ .)

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