
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
In a diagram, a square has a perimeter of 64 units and is adjoined on one side by a rectangle of width 8 units. A triangle with a height of 64 units also shares its base with the rectangle's length. If the square and the triangle have the same area, find the value of the rectangle's length, denoted as $y$.

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