
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
Simplify the following fractions:
a) $\frac{3 a^{4} c+2 a^{4} d-3 b^{4} c-2 b^{4} d}{\left[9 c^{2}(a-b)-4 d^{2}(a-b)\right]\left[(a+b)^{2}-2 a b\right]}$,
b) $\frac{a^{2}+b^{2}+c^{2}+2 a b+2 a c+2 b c}{a^{2}-b^{2}-c^{2}-2 b c}$,
c) $\frac{a^{2}-3 a b+a c+2 b^{2}-2 b c}{a^{2}-b^{2}+2 b c-c^{2}}$.

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