
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
If $y = x^3 + 3px^2 + 3qx + r$, find the value of $r$ such that when $x = -p$, $y$ is minimized and equals $-27$.
**A)** $-27 - 3p^3 + 2pq$  
**B)** $27 + 2p^3 - 3pq$  
**C)** $-27 - 2p^3 + 3pq$  
**D)** $-27 - 2p^2 + 3pq$

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