
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 sides of triangle $ABC$ are distinct, with $BC = a$ being the smallest and $AB = c$ the largest. Determine the segments on the perimeter of the triangle where the points $D, E, F, G, H, J$ (as specified in Exercise 715) cannot lie, in order to ensure that each designated point falls within the interior of its respective side segment.

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