
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
The median $AA_{0}$ of triangle $ABC$ is extended from point $A_{0}$ perpendicularly to side $BC$ outside of the triangle. Let the other end of the constructed segment be denoted as $A_{1}$. Similarly, points $B_{1}$ and $C_{1}$ are constructed. Find the angles of triangle $A_{1}B_{1}C_{1}$, given that the angles of triangle $ABC$ are $30^{\circ}, 30^{\circ}$, and $120^{\circ}$.

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