
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
In a triangle, if one interior angle is three times another interior angle, we call such a triangle a "three times angle triangle." For example, a triangle with interior angles of $120^{\circ}$, $40^{\circ}$, and $20^{\circ}$ is a "three times angle triangle."  
$(1)$ In triangle $\triangle ABC$, if $\angle A = 35^{\circ}$ and $\angle B = 40^{\circ}$, is $\triangle ABC$ a "three times angle triangle"? Why?  
$(2)$ If $\triangle ABC$ is a "three times angle triangle" and $\angle B = 60^{\circ}$, find the degree measure of the smallest interior angle in $\triangle ABC$.

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