
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
The angles $\alpha, \beta, \gamma$ of a triangle have the property that $\operatorname{ctg} \frac{\alpha}{2}, \operatorname{ctg} \frac{\beta}{2}, \operatorname{ctg} \frac{\gamma}{2}$ are consecutive integers. What is the largest angle of the triangle?

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