
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
The real numbers \( x \) and \( y \) satisfy the equations \( 4^{y}=\frac{1}{8(\sqrt{2})^{x+2}} \) and \( 9^{x} \times 3^{y}=3 \sqrt{3} \). What is the value of \( 5^{x+y} \) ?

A) \( 5 \sqrt{5} \)

B) 5

C) \( \sqrt{5} \)

D) \( \frac{1}{5} \)

E) \( \frac{1}{\sqrt{5}} \)

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