
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 $B_{1}$ and $A_{1}$ be the midpoints of the sides $C A$ and $C B$ of triangle $ABC$ respectively, and let $O$ be the center of the inscribed circle of the triangle. What is the condition for $\angle B_{1} O A_{1} = \angle BAC + \angle ABC$ to hold?

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