
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
There are four lines on a plane, with any two of them intersecting and no three being concurrent. Each intersection on a line divides it into two non-overlapping segments, resulting in a total of eight non-overlapping segments.

(1) Is it possible for these eight segments to have lengths of 1, 2, ..., 8 respectively? Please provide a brief explanation.

(2) Construct an example where the lengths of these eight segments are distinct positive integers.

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