
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 $ABC$, $AB = AC$, and point $D$ is the midpoint of both $\overline{BC}$ and $\overline{AE}$. $\overline{CE}$ is 15 units long. Calculate the length of $\overline{BD}$. Additionally, if the height from point $A$ perpendicular to $BC$ is 12 units, find the area of triangle $ABC$. Express $\overline{BD}$ as a decimal to the nearest tenth and the area rounded to the nearest whole number.

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