
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
For a certain complex number $d$, the polynomial
\[Q(x) = (x^2 - 3x + 3)(x^2 - dx + 5)(x^2 - 5x + 10)\]
has exactly 5 distinct roots. What is $|d|$?
**A)** $\sqrt{24}$
**B)** $\sqrt{26}$
**C)** $\sqrt{28}$
**D)** $\sqrt{30}$

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