
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 $n$ in base 8, from left to right. For example, $b_4$ in base 8 is 1234, and $b_{12}$ in base 8 would be $1,2,3,4,5,6,7,10,11,12,13,14$. For $1 \le k \le 100$, how many $b_k$ are divisible by 7?

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