
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
There are 50 square frames resting on one side of a horizontal line e. Each frame is hinged at the lower left corner to the lower right corner of its left neighbor. Each frame's side length equals the diagonal of its right neighbor. The smallest frame is fixed and considered as the first one, and the rest are, in their entirety, rotated $45^\circ$ counterclockwise. Then the second frame is fixed, and similarly step by step, each following frame is rotated to form a $45^\circ$ angle at each hinge. In the final position, which numbered frames share a common point with the line e?

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