
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 circle with radius 1 is situated between two parallel lines, touching both lines. An isosceles triangle is positioned such that its base lies on one of the lines, and its vertex is on the other line. It is known that the triangle and the circle have exactly one common point, and this point lies on the inscribed circle of the triangle. Find the radius of the inscribed circle of the triangle.

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