
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
Let  $x,y\in\mathbb{R}$  be such that  $x = y(3-y)^2$  and  $y = x(3-x)^2$ . Find all possible values of  $x+y$ .


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