
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
As shown in the diagram, in $\triangle ABC$, $\angle A = 60^\circ$, $AB > AC$, point $O$ is the circumcenter, the two altitudes $BE$ and $CF$ intersect at point $H$. Points $M$ and $N$ are respectively on segments $BH$ and $HF$, and satisfy $BM = CN$. Find the value of $\frac{MH + NH}{OH}$.

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