
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 \( n \) be the number of integer values of \( x \) such that the polynomial \( Q = x^4 + 8x^3 + 20x^2 + kx + 64 \) is the square of an integer for \( k = 16 \). Find the value of \( n \).
**A)** 0
**B)** 1
**C)** 2
**D)** 3
**E)** 4

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