
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 regular  $ n\minus{}$ gon  $ A_1A_2A_3 \cdots A_k \cdots A_n$  inscribed in a circle of radius  $ R$  is given. If  $ S$  is a point on the circle, calculate \[ T \equal{} \sum^n_{k\equal{}1} SA^2_k.\]

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