
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   $$ \sin^2{x} + \cos^2{y} = y^4.  $$     $$ \sin^2{y} + \cos^2{x} = x^2.  $$  *A. Khrabov*

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