
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 $a_1$, $a_2$, ..., $a_n$ be positive integers, among which there are at least five distinct values. If for any $i$, $j$ ($1 \leq i < j \leq n$), there exist $k$, $l$ ($k \neq l$, and different from $i$ and $j$) such that $a_i + a_j = a_k + a_l$, then the minimum value of $n$ is.

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