
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 the angles of a triangle be $\alpha, \beta, \gamma$. Find the smallest and largest values of $\alpha$ (rounded to the nearest tenth of a degree) such that $\beta - \gamma = 30^{\circ}$, and

$$
10 \sin \alpha \sin \beta \sin \gamma - 2 \sin 60^{\circ}\left(\sin ^{2} \alpha + \sin ^{2} \beta + \sin ^{2} \gamma\right) > 0
$$

knowing that the values of $\alpha$ between $23.0^{\circ}$ and $100.0^{\circ}$ satisfy the inequality.

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