
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
Solve for $x$ and $y$ if $3x^2 - 9y^2 = 0$, and also $x + y = 5$.
A) $(\frac{15 - 5\sqrt{3}}{2}, \frac{5\sqrt{3} - 5}{2})$
B) $(\frac{-15 - 5\sqrt{3}}{2}, \frac{5 + 5\sqrt{3}}{2})$
C) $(\frac{15\sqrt{3} - 5}{2}, \frac{5 - 5}{2})$
D) $(\frac{-15\sqrt{3} + 5}{2}, \frac{5\sqrt{3} + 5}{2})$

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