
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
Let  $a$  be the sum of the numbers: $99 \times 0.9$  $999 \times 0.9$  $9999 \times 0.9$  $\vdots$  $999\cdots 9 \times 0.9$ where the final number in the list is  $0.9$  times a number written as a string of  $101$  digits all equal to  $9$ .
Find the sum of the digits in the number  $a$ .

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