
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 is tangent to one leg of an isosceles right triangle and passes through the vertex of the opposite acute angle. Find the radius of the circle if its center is on the hypotenuse of the triangle and a leg of the triangle is equal to $a$.

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