
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 5 line segments with lengths 3, 5, 6, 9, and 10, respectively. Calculate the maximum number of different triangles that can be formed by selecting any three of these line segments.

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