
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
In triangle \( ABC \), altitudes \( AD \), \( BE \), and \( CF \) intersect at the orthocenter \( H \). If \( \angle ABC = 58^\circ \) and \( \angle ACB = 20^\circ \), find the measure of \( \angle BHC \), in degrees.

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