
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
Given the following 4 by 4 square grid of points, determine the number of ways we can label ten different points \(A, B, C, D, E, F, G, H, I, J\) such that the lengths of the nine segments \(AB, BC, CD, DE, EF, FG, GH, HI, IJ\) are in strictly increasing order.

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