
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
Define a "digitized number" as a ten-digit number  $a_0a_1\ldots a_9$  such that for  $k=0,1,\ldots, 9$ ,  $a_k$  is equal to the number of times the digit  $k$  occurs in the number.  Find the sum of all digitized numbers.

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