
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
A stick of length \( L \) is divided into 8, 12, and 18 equal segments using red, blue, and black lines, respectively. The stick is then cut at each marked point. How many segments will be obtained in total? What is the length of the shortest segment?

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