
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 base of a pyramid is an equilateral triangle with side length \(a\). The height of the pyramid passes through the midpoint of one of the sides of the base and is equal to \(\frac{3a}{2}\). Find the radius of the sphere circumscribed about the pyramid.

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