
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
$$
\frac{\operatorname{ctg} \alpha \cdot \sin \alpha}{\sin \beta \cdot \sin \gamma}=\frac{2}{3} \quad \text{and} \quad \alpha + \beta + \gamma = 180^{\circ}
$$

then

$$
\operatorname{tg} \beta \operatorname{tg} \gamma = 3
$$

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