
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
On the sides \(AB\) and \(BC\) of an isosceles triangle \(ABC\), points \(M\) and \(N\) are located respectively, such that \(\frac{AM}{BM}=m\) and \(\frac{CN}{BN}=n\). The line \(MN\) intersects the altitude \(BD\) of the triangle at point \(O\). Find the ratio \(\frac{DO}{BO}\).

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