
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 center $O$ is tangent to the coordinate axes and to the hypotenuse of a $45^\circ$-$45^\circ$-$90^\circ$ triangle $ABC$, where $AB=2$. The triangle is positioned such that its hypotenuse is horizontal. Calculate the radius of the circle.
A) 1.5  
B) 1.75  
C) 2  
D) 2.25  
E) 2.5

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