
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 rectangles \( S_1 \) and \( S_2 \) are drawn on a set of coordinate axes. \( S_1 \) has vertices at \((0, y)\), \((x, y)\), \((x, 4)\), and \((0, 4)\), where \( x < 9 \) and \( y < 4 \). \( S_2 \) has vertices at \((x, 0)\), \((9,0)\), \((9, y)\), and \((x, y)\). The rectangles are equal in area. What is the value of \( \frac{360x}{y} \)?

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