
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
The centers of four spheres with radius $r \left( r < \frac{1}{\sqrt{2}} \right)$ are located at the vertices of an isosceles right triangle with legs equal to 2, and at the midpoint of its hypotenuse. Find the radius of the sphere that touches these four spheres.

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