
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
One end of the diameter of a semicircle coincides with the vertex of the angle at the base of an isosceles triangle, and the other end belongs to this base. Find the radius of the semicircle, given that it touches one of the legs of the triangle and divides the other leg into segments of 5 cm and 4 cm, measured from the base.

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