
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
173_ is a four-digit number. The mathematics teacher says: "If I insert 3 different digits into the blank spaces, the resulting 3 four-digit numbers will be divisible by 9, 11, and 6, respectively." What is the sum of the 3 digits that the teacher inserts?

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