
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 is a wire 150 cm long that needs to be cut into several pieces, with the requirement that the length of each piece is an integer not less than 1. If any three pieces cannot form a triangle, what is the maximum number of pieces the wire can be cut into, and how many different ways are there to cut it?

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