
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
The positive real numbers  $x$  and  $y$  satisfy the relation  $x + y = 3 \sqrt{xy}$ . Find the value of the numerical expression   $$ E=\left| \frac{x-y}{x+y}+\frac{x^2-y^2}{x^2+y^2}+\frac{x^3-y^3}{x^3+y^3}\right|. $$  

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