
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
Let \( \mathrm{ABC} \) be a triangle with sides \( AB = 7 \), \( BC = 8 \), and \( AC = 9 \). A unique circle can be drawn touching the side \( AC \) and the lines \( BA \) produced and \( BC \) produced. Let \( D \) be the center of this circle. Find the value of \( BD^2 \).

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