
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
For a triangle with side lengths $1005, 1006, 1007$, if $T_{n+1}$ is the triangle with side lengths obtained by replacing the side lengths of $T_n$ with the tangents from the incircle to the sides of $T_n$, determine the perimeter of the last triangle in the sequence $(T_n)$.

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