
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
Find \(\sin \alpha\) if \(\cos \alpha = \operatorname{tg} \beta\), \(\cos \beta = \operatorname{tg} \gamma\), \(\cos \gamma = \operatorname{tg} \alpha\) \((0 < \alpha < \frac{\pi}{2}, 0 < \beta < \frac{\pi}{2}, 0 < \gamma < \frac{\pi}{2})\).

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