
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
A rectangle $EFGH$ has vertices $E$(0, 0), $F$(0, $y$), $G$($x$, $y$), and $H$($x$, 0), with $x$, $y$ > 0. The area of the rectangle is 36 square units and its perimeter is 30 units. Determine the dimensions $x$ and $y$.

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