
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
Given $T_1$ is a triangle with side lengths $1011$, $1012$, and $1013$, and for each $n \geq 1$, $T_{n+1}$ is a triangle with side lengths $AD$, $BE$, and $CF$, where $D, E$, and $F$ are the midpoints of the sides $AB$, $BC$, and $AC$, respectively, determine the perimeter of the last possible triangle $T_n$ in this sequence.

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