
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 that $\Gamma$ is a circle with radius 1, a set $T$ composed of triangles is called "good" if and only if it meets the following conditions:
1. Every triangle in $T$ is an inscribed triangle in the circle $\Gamma$.
2. No two triangles in $T$ have common internal points.

Find all positive real numbers $t$ such that for every positive integer $n$, there exists a good set consisting of $n$ triangles, and the perimeter of each triangle is greater than $t$.

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