
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 $T_{0}$ is cut into two non-congruent rectangles, $T_{1}$ and $T_{1}^{\prime}$, such that the two resulting parts are similar. This process is repeated on the rectangle $T_{1}$, then on one of the resulting parts, and so on. Is there a rectangle $T_{0}$ for which this procedure can be continued indefinitely?

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