
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 system of equations:  $$ \left\{ \begin{array}{l}
({x^2} + y)\sqrt {y - 2x}  - 4 = 2{x^2} + 2x + y
{x^3} - {x^2} - y + 6 = 4\sqrt {x + 1}  + 2\sqrt {y - 1} 
\end{array} \right.(x,y \in \mathbb{R}). $$  

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