
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 \( b_1 = 1, b_2 = 2, b_3 = 1 \). For \( n > 3 \), let \( b_n \) be the number of real numbers \( y \) such that
\[
y^4 - 3b_{n-1}y^2 + b_{n-2}b_{n-3} = 0.
\]
Compute the sum \( b_1 + b_2 + b_3 + \ldots + b_{15} \).

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