
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 circular sheet of paper with a radius of $10$ cm is cut into four congruent sectors. What is the height of the cone that can be formed by rolling one of these sectors until the edges meet? Also calculate the surface area of the cone in simplest form.

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