
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
Let ABCD be a unit square. Draw a quadrant of a circle with A as centre and B;D
as end points of the arc. Similarly, draw a quadrant of a circle with B as centre and
A;C as end points of the arc. Inscribe a circle ? touching the arc AC internally, the
arc BD internally and also touching the side AB. Find the radius of the circle ?.

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