
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 the following system of equations:

$$
\begin{array}{r}
x^{2} + y \sqrt{x y} = 105 \\
y^{2} + x \sqrt{y x} = 70
\end{array}
$$

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