
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
Evaluate and simplify the fraction $\frac{a^2b^2 + 2a^2bc + a^2c^2 - b^4}{a^4 - b^2c^2 + 2abc^2 + c^4}$ given that none of $a, b, c$ are zero and $a^2 + b^2 + c^2 \neq 0$.

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