
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

a) \(\operatorname{ctg}(\alpha / 2)+\operatorname{ctg}(\beta / 2)+\operatorname{ctg}(\gamma / 2) \geq 3 \sqrt{3}\).

b) For an acute-angled triangle

\[
\operatorname{tg} \alpha+\operatorname{tg} \beta+\operatorname{tg} \gamma \geq 3 \sqrt{3}
\]

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