
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
The following process is applied to each positive integer: the sum of its digits is subtracted from the number, and the result is divided by  $9$ . For example, the result of the process applied to  $938$  is  $102$ , since  $\frac{938-(9 + 3 + 8)}{9} = 102.$  Applying the process twice to  $938$  the result is  $11$ , applied three times the result is  $1$ , and applying it four times the result is  $0$ . When the process is applied one or more times to an integer  $n$ , the result is eventually  $0$ . The number obtained before obtaining  $0$  is called the *house* of  $n$ .

How many integers less than  $26000$  share the same *house* as  $2012$ ?

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