
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 \( 1015, 1016, \) and \( 1017 \). For \( n \geq 1 \), if \( T_n = \triangle ABC \) where \( D, E, \) and \( F \) are points of tangency of the incircle of \( \triangle ABC \) to sides \( AB, BC, \) and \( AC \) respectively, \( T_{n+1} \) is a triangle formed by the side lengths \( AD, BE, \) and \( CF \) if it exists. Determine the perimeter of the last existing triangle in this sequence.

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