
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 \( a_n \) be the number written with \( 2n \) nines. For example, \( a_0 = 9 \), \( a_1 = 99 \), \( a_2 = 9999 \). Let \( b_n = \sum_{i=0}^n a_i \). Find the sum of the digits of \( b_n \).

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