
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
$(1)$ If real numbers $a$ and $b$ satisfy $\sqrt{a-1}+\sqrt{{(9+b)}^{2}}=0$, find the cube root of $a+b$;<br/>$(2)$ Given real numbers $x$ and $y$ satisfy $y=\sqrt{x-5}-\sqrt{5-x}+2$, find the square root of $x^{y}$.

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