
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
Read the example and answer the question:<br/>Example: Let $a$ and $b$ be rational numbers, satisfying $a+\sqrt{2}b=3-2\sqrt{2}$. Find the value of $a+b$.<br/>Solution: From the given conditions, we have $a-3+\left(b+2\right)\sqrt{2}=0$. Since $a$ and $b$ are rational numbers, $a-3$ and $b+2$ are also rational numbers. Therefore, $a=3$ and $b=-2$, so $a+b=3+(-2)=1$.<br/>Question: Let $x$ and $y$ be rational numbers, satisfying $x^{2}-2y+\sqrt{5}y=10+3\sqrt{5}$. Find the value of $x^{y}$.

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