
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 $y$ satisfy the equation
\[\sqrt{\log{x}} + \sqrt{\log{y}} + 3\log \sqrt{x} + 3\log \sqrt{y} = 150\]
where all terms are positive integers, and log denotes the base 10 logarithm. Determine the value of $xy$.
A) $10^{170}$
B) $10^{132}$
C) $10^{129}$
D) $10^{140}$
E) $10^{130}$

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