
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
Given the list of equations $\text{(A)}\: (x-5)^3 = 0$, $\text{(B)}\: 2^{x+1} = 1$, $\text{(C)}\: \log_2(x+4) = -3$, $\text{(D)}\: \sqrt{3x+1} = 2$, $\text{(E)}\: x^2 + 2x + 2 = 0$, determine which equation does NOT have any real solutions.

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