
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
Let \(T_1\) be a triangle with side lengths \(2021\), \(2022\), and \(2023\). For \(n \geq 1\), if \(T_n = \Delta ABC\) and \(D, E\), and \(F\) are the points of tangency of the incircle of \(\Delta ABC\) to the sides \(AB\), \(BC\), and \(AC\) respectively, then \(T_{n+1}\) is a triangle with side lengths \(AD\), \(BE\), and \(CF\), if it exists. Calculate the perimeter of the last triangle in the sequence \(T_n\).
A) \(\frac{1516.5}{256}\) 
B) \(\frac{1516.5}{128}\) 
C) \(\frac{1516.5}{512}\) 
D) \(\frac{1516.5}{1024}\) 
E) \(\frac{1516.5}{2048}\)

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