
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 \( A B C \), angle \( A \) is equal to \( \arccos \frac{7}{8} \), \( B C = a \), and the altitude dropped from vertex \( A \) is equal to the sum of the other two altitudes. Find the area of triangle \( A B C \).

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