
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 a circle $O$ with an inscribed triangle $\triangle ABC$, let $C_1$, $A_1$, and $B_1$ be the midpoints of arcs $\overparen{AB}$, $\overparen{BC}$, and $\overparen{CA}$, respectively, forming an inscribed triangle $\triangle A_1 B_1 C_1$. Next, let $C_2$, $A_2$, and $B_2$ be the midpoints of arcs $\overparen{A_1B_1}$, $\overparen{B_1C_1}$, and $\overparen{C_1A_1}$, respectively, forming another inscribed triangle $\triangle A_2 B_2 C_2$. As $n$ tends to infinity, what is the trend in the angles of triangle $\triangle A_n B_n C_n$?

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