
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
Each of two sides of a triangle is divided into six equal parts; the corresponding division points are connected by line segments. Find the sum of the lengths of these segments if the third side of the triangle is equal to 12.

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