
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
Solve the following equation:

$$
2x^{4} + 2y^{4} - 4x^{3}y + 6x^{2}y^{2} - 4xy^{3} + 7y^{2} + 7z^{2} - 14yz - 70y + 70z + 175 = 0.
$$

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