
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 triangle with sides  $a,b,c$  and perimeter  $2p$  is given. Is possible, a new triangle with sides  $p-a$ ,  $p-b$ ,  $p-c$  is formed. The process is then repeated with the new triangle. For which original triangles can this process be repeated indefinitely?

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