
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 condition for three line segments to form a triangle is: the sum of the lengths of any two line segments is greater than the length of the third line segment. Now, there is a wire 144cm long, and it needs to be cut into $n$ small segments ($n>2$), each segment being no less than 1cm in length. If any three of these segments cannot form a triangle, then the maximum value of $n$ is ____.

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