
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
Given a positive integer  $N$  (written in base  $10$ ), define its *integer substrings* to be integers that are equal to strings of one or more consecutive digits from  $N$ , including  $N$  itself. For example, the integer substrings of  $3208$  are  $3$ ,  $2$ ,  $0$ ,  $8$ ,  $32$ ,  $20$ ,  $320$ ,  $208$ ,  $3208$ . (The substring  $08$  is omitted from this list because it is the same integer as the substring  $8$ , which is already listed.)

What is the greatest integer  $N$  such that no integer substring of  $N$  is a multiple of  $9$ ? (Note:  $0$  is a multiple of  $9$ .)

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