
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 set of positive numbers is said to have the triangle property if it includes three distinct elements that can be the lengths of the sides of a triangle with a positive area. Envision sets $\{7, 8, 9, \ldots, n\}$ of consecutive positive integers where every ten-element subset possesses the triangle property. What is the maximum possible value of $n$?

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