
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 \( b_{10} = 10 \), and for each positive integer \( n > 10 \), let \( b_n = 150b_{n - 1} + n^2 \). Find the least positive \( n > 10 \) such that \( b_n \) is a multiple of 135.

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