
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
The diagram below shows  $\vartriangle ABC$  with point  $D$  on side  $\overline{BC}$ . Three lines parallel to side  $\overline{BC}$  divide segment  $\overline{AD}$  into four equal segments. In the triangle, the ratio of the area of the shaded region to the area of the unshaded region is  $\frac{49}{33}$  and  $\frac{BD}{CD} = \frac{m}{n}$  , where  $m$  and  $n$  are relatively prime positive integers. Find  $m + n$ .
![Image](https://cdn.artofproblemsolving.com/attachments/2/8/77239633b68f073f4193aa75cdfb9238461cae.png)

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