
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
In the triangular pyramid \( SABC \), it is known that \( AB = AC = 10 \) and \( BC = 16 \). The height of the pyramid dropped from the vertex \( S \) passes through the vertex \( B \) and is equal to 4. Find the total surface area of the pyramid and the radius of the sphere inscribed in the pyramid.

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