
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 fraction:

$$
\frac{6 a^{2}-2 b^{2}+6 c^{2}+a b-13 a c-4 b c-18 a-5 b+17 c+12}{4 a^{2}-b^{2}+9 c^{2}-12 a c-16 a+24 c+16}
$$

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