
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
Determine all integers $n>3$ for which there exist $n$ points $A_{1}, A_{2}, \cdots, A_{n}$ in the plane and real numbers $r_{1}, r_{2}, \cdots, r_{n}$ such that the following conditions are satisfied:
1. No three points among $A_{1}, A_{2}, \cdots, A_{n}$ are collinear.
2. For every triple $i, j, k (1 \leqslant i<j<k \leqslant n)$, the area of the triangle $\triangle A_{i} A_{j} A_{k}$ is equal to $r_{i} + r_{j} + r_{k}$.

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