
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 squares of integers 1 to $n$ from left to right. For example, $b_4 = 1491625$ (since $1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16$). For $1 \le k \le 50$, how many $b_k$ are divisible by 9?

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