
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  $ABC$  be a triangle and let  $\Omega$  be its circumcircle. The internal bisectors of angles  $A, B$  and  $C$  intersect  $\Omega$  at  $A_1, B_1$  and  $C_1$ , respectively, and the internal bisectors of angles  $A_1, B_1$  and  $C_1$  of the triangles  $A_1 A_2 A_ 3$  intersect  $\Omega$  at  $A_2, B_2$  and  $C_2$ , respectively. If the smallest angle of the triangle  $ABC$  is  $40^{\circ}$ , what is the magnitude of the smallest angle of the triangle  $A_2 B_2 C_2$  in degrees?

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