
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 $\mathrm{AA}_{0}$ of triangle $\mathrm{ABC}$ is extended from point $\mathrm{A}_{0}$ perpendicularly to side $\mathrm{BC}$ outside the triangle. The other end of the constructed segment is denoted as $\mathrm{A}_{1}$. Similarly, points $\mathrm{B}_{1}$ and $\mathrm{C}_{1}$ are constructed. Find the angles of triangle $\mathrm{A}_{1} \mathrm{~B}_{1} \mathrm{C}_{1}$, given that the angles of triangle $\mathrm{ABC}$ are $30^{\circ}, 30^{\circ}$, and $120^{\circ}$.

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