
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
We have three congruent right-angled triangular pieces of paper. Any of these pieces can be cut in half along its height. From the resulting triangles, any one can again be cut in half along its height, and this process can be continued. What can be the ratio of the legs if we know that during the process, there will always be two congruent triangles?

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