
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
Solve for $y$ in terms of $b$, where $b \neq 0$, given the determinant:
\[
\begin{vmatrix}
y + b & -y & y \\
-y & y + b & -y \\
y & -y & y + b
\end{vmatrix} = 0.
\]

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