
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
Let $px^2+qx+r=0$ have roots $u$ and $v$. The quadratic equation with roots $2pu + 3q$ and $2pv + 3q$ is:
**A)** \(x^2 - 4qx + 4pr = 0\)
**B)** \(x^2 - 4qx + 3pr + 2q^2 = 0\)
**C)** \(x^2 - 4qx + 4pr + 3q^2 = 0\)
**D)** \(x^2 - 3qx + 2pr + q^2 = 0\)
**E)** \(x^2 - 2qx + pr + q^2 = 0\)

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