
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
Consider the equation \( x = K^3 (x^3 - 3x^2 + 2x + 1) \). For what real values of \( K \) does this equation have real roots?
A) \( K > 0 \)
B) \( K = 0 \)
C) \( K < 0 \)
D) All real \( K \)
E) No real \( K \)

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