
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 \( \triangle ABC \), \(\angle A = 60^\circ\) and \( AB > AC \). Point \( O \) is the circumcenter, and the two altitudes \( BE \) and \( CF \) intersect at point \( H \). Points \( M \) and \( N \) are on segments \( BH \) and \( HF \) respectively, such that \( BM = CN \). Find the value of \((MH + NH) / OH\).

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