
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
Determine the greatest common divisor of the following two expressions:

$$
6 x^{4} + 5 x^{3} y + 5 x^{2} y^{2} + 10 x y^{3} + 4 y^{4}
$$

$$
8 x^{4} + 6 x^{3} y - x^{2} y^{2} + 3 x y^{3} + 2 y^{4}
$$

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