
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
Given $a \neq b, a^3 - b^3 = 25y^3$, and $a - b = y$, determine the expressions for $b$ in terms of $y$.
**A)** $b = -\frac{1 - \sqrt{33}}{2}y$  
**B)** $b = -\frac{1 + \sqrt{33}}{2}y$  
**C)** $b = \frac{1 - \sqrt{33}}{2}y$  
**D)** $b = \frac{1 + \sqrt{33}}{2}y$

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