
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
Kiran needs to solve the quadratic equation \(16x^2 + 32x - 512 = 0\) using the method of completing the square. In this process, she derives an equivalent equation \((x + p)^2 = q\), where \(p\) and \(q\) are constants. Determine \(q\).

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