
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 constructed on the longer leg of a right triangle as its diameter. Determine the radius of this circle if the shorter leg of the triangle is 7.5 cm, and the length of the chord connecting the vertex of the right angle with the point where the hypotenuse intersects the circle is 6 cm.

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