
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 right triangle with a hypotenuse of length 1, a circle is inscribed. A line is drawn through the points where the circle touches the triangle's legs.

What is the possible length of the segment that the circle circumscribed around the original triangle cuts on this line?

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