
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 positive integers \( a_{1}, a_{2}, \ldots, a_{2023} \) such that
$$
a_{k}=\sum_{i=1}^{2023}\left|a_{k}-a_{i}\right|
$$
for all \( 1 \leq k \leq 2023 \), find the minimum possible value of \( a_{1}+a_{2}+\cdots+a_{2023} \).

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