
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
Consider the fraction $\frac{4a^2 + 2c^2 - 4b^2 - 8bc}{3a^2 + 6ac - 3c^2 - 6ab}$. Is it reducible to a simpler form, and if so, to which of the following?
A) $\frac{1}{3} \frac{a-2b+c}{a-b+c}$
B) $\frac{4}{3} \frac{(a-2b+c)(a-c)}{(a-b+c)(a-b-c)}$
C) $\frac{3}{4} \frac{(a+c-b)(a+c)}{(a+c+b)(a-c-b)}$
D) $\frac{a^2-2ab+c^2}{a^2+2ac-c^2}$

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