
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 $\triangle ABC$, point $D$ is inside $\triangle ABC$ such that it creates two line segments $AD$ and $DC$. The lengths are $AD=5$ and $DC=7$. Calculate the ratio of the area of $\triangle ABD$ to the area of $\triangle BDC$ given that the triangles share the same height from $B$.

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