
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
The sides of 100 identical equilateral triangles are painted in 150 colors such that each color is used to paint exactly two sides. If two triangles are joined by sides painted the same color, the resulting rhombus is called a good rhombus. Petya wants to assemble as many good rhombuses as possible from these triangles, with each triangle used in at most one rhombus. What is the maximum number of good rhombuses Petya can guarantee regardless of how the triangles are painted?

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