
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 surface area of a sphere with radius $r$ is $4\pi r^2$. Consider a segmented hemisphere consisting of a spherical cap with height $6$ cm less than the radius of the original hemisphere $(10$ cm$)$ and the remaining part is a circular segment (base of the cap is $6$ cm). Calculate the combined surface area of this composite shape. Express your answer in terms of $\pi$.

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