
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 $\triangle ABC$ be a triangle with angles $\alpha = 59^\circ$, $\beta = 60^\circ$, and $\gamma = 61^\circ$. For each positive integer $n$, define $\alpha_n = 59^\circ + n\cdot 0.02^\circ$, $\beta_n = 60^\circ$, and $\gamma_n = 61^\circ - n\cdot 0.02^\circ$. What is the least positive integer $n$ for which $\triangle ABC$ with angles $\alpha_n$, $\beta_n$, and $\gamma_n$ is obtuse?

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