
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 "nearly regular" triangle $H_{0}$ has angles of $59.5^\circ$, $60^\circ$, and $60.5^\circ$. Consider the following sequence of triangles. Let $H_{1}$ be the pedal triangle of $H_{0}$, $H_{2}$ be the pedal triangle of $H_{1}$, and so on. What position in the sequence will the first obtuse-angled triangle appear?

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