
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
For any given triangle  $A_0B_0C_0$  consider a sequence of triangles constructed as follows: 
a new triangle  $A_1B_1C_1$  (if any) has its sides (in cm) that equal to the angles of  $A_0B_0C_0$  (in radians). Then for  $\vartriangle  A_1B_1C_1$   consider a new triangle  $A_2B_2C_2$  (if any) constructed in the similar พay, i.e.,  $\vartriangle A_2B_2C_2$  has its sides (in cm) that equal to the angles of  $A_1B_1C_1$  (in radians), and so on.
Determine for which initial triangles  $A_0B_0C_0$  the sequence never terminates.

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