
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
Let $\triangle A_0B_0C_0$ be an isosceles triangle with $\angle B_0A_0C_0 = 50^\circ$, $\angle A_0B_0C_0 = 65^\circ$, and $\angle C_0A_0B_0 = 65^\circ$. For each positive integer $n$, define $\triangle A_nB_nC_n$ such that $A_n$ is the intersection of angle bisectors of $\angle B_{n-1}C_{n-1}A_{n-1}$, similarly for $B_n$ and $C_n$. Determine the smallest $n$ where $\triangle A_nB_nC_n$ has all angles less than or equal to $60^\circ$.
A) 2
B) 3
C) 4
D) 5
E) 6

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