
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 \( b_n \) be the number obtained by writing the integers from 1 to \( n \) from left to right. For example, \( b_4 = 1234 \) and \( b_{12} = 123456789101112 \). Let \( g(b_n) \) be the sum of the squares of the digits of \( b_n \). For \( 1 \le k \le 50 \), how many \( b_k \) are divisible by 6?

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