
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 rod of length $L$ is divided into 8, 12, and 18 equal parts using red, blue, and black lines, respectively. If the rod is cut at all the marked points, how many segments will be obtained in total? Additionally, what is the length of the shortest segment?

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