
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
Find all solutions  $ (x,y)\in \mathbb{R}\times\mathbb R$  of the following system:  $ \begin{cases}x^3 \plus{} 3xy^2 \equal{} 49, 
x^2 \plus{} 8xy \plus{} y^2 \equal{} 8y \plus{} 17x.\end{cases}$ 

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