
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
Positive real numbers $x$ and $y$ have the property that
\[
\sqrt{\log{x}} + \sqrt{\log{y}} + \log \sqrt{x} + \log \sqrt{y} + 10 = 120
\]
where all terms on the left are positive integers, and log denotes the base 10 logarithm. What is $xy$?
A) $10^{90}$
B) $10^{100}$
C) $10^{110}$
D) $10^{120}$

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