
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
Find such \( n \) and such numbers \( a_{i}, b_{i}, c_{i} \) \((i=1,2, \ldots, n)\) that the condition

\[ 
\sum_{i=1}^{n}\left|a_{i} x+b_{i} y+c_{i}\right|=10 
\]

is satisfied, such that the pairs \((x, y)\) plotted in the coordinate system form the points of a regular octagon.

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