
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
Find the sum of squares of all distinct complex numbers \(x\) satisfying the equation
$$
0 = 4x^{10} - 7x^{9} + 5x^{8} - 8x^{7} + 12x^{6} - 12x^{5} + 12x^{4} - 8x^{3} + 5x^{2} - 7x + 4.
$$

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