
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
What are the solutions of the simultaneous equations:
$$
\begin{aligned}
3 x^{2}+x y-2 y^{2} & =-5 \\
x^{2}+2 x y+y^{2} & =1 ?
\end{aligned}
$$

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