
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 semicircle is inscribed in a triangle, with the semicircle touching the base and the diameter (with its ends on the lateral sides of the triangle) parallel to the base. Find the radius of the semicircle if the base of the triangle is $a$ and the height is $h$.

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