
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
What remains of the rectangle? A golden rectangle is a rectangle whose sides \(a\) and \(b\) are in the golden ratio, that is, they satisfy the equation

\[ 
a: b = b : (a - b) 
\]

Imagine this rectangle is cut out of paper and placed on the table with its longer side facing us. We cut off the largest possible square from the left side of the rectangle; the remaining part will still be a golden rectangle. We then move to the left side of the table to again have the longer side of the rectangle facing us, and we repeat the same procedure with the new rectangle as with the previous one. We continue this process, moving around the table clockwise and cutting off squares in turn. Every point of the rectangle, except one, will be cut off sooner or later. Determine the position of this exceptional point.

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