
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
Points $A_{1}, B_{1}, C_{1}$ are the points of intersection of the extensions of the altitudes of the acute-angled triangle $ABC$ with the circumcircle of $ABC$. The incircle of triangle $A_{1} B_{1} C_{1}$ touches one of the sides of $ABC$, and one of the angles of triangle $ABC$ is $40^{\circ}$. Find the other two angles of triangle $ABC$.

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