
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 numbers \( x \) and \( y \) are such that \( 3^{x} + 3^{y+1} = 5 \sqrt{3} \) and \( 3^{x+1} + 3^{y} = 3 \sqrt{3} \). What is the value of \( 3^{x} + 3^{y} \)?

A) \( \sqrt{3} \)  
B) \( 2 \sqrt{3} \)  
C) \( 3 \sqrt{3} \)  
D) \( 4 \sqrt{3} \)  
E) \( 5 \sqrt{3} \)

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