
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
For any positive integer  $x$ , let  $S(x)$  be the sum of the digits of  $x$ , and let  $T(x)$  be  $|S(x+2)-S(x)|.$   For example,  $T(199)=|S(201)-S(199)|=|3-19|=16.$   How many values  $T(x)$  do not exceed 1999?

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