
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 $1201, 1203, 1205$. For $n \ge 1$, if $T_n = \triangle ABC$ and $D, E, F$ are the points of tangency of the incircle of $\triangle ABC$ to the sides $AB, BC, AC$, respectively, then $T_{n+1}$ is a triangle with side lengths $AD, BE, CF$, if it exists. What is the perimeter of the last triangle in the sequence $(T_n)$?
A) $\frac{903}{64}$
B) $\frac{903}{128}$
C) $\frac{903}{256}$
D) $\frac{1809}{256}$
E) $\frac{1809}{128}$

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