
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 center of the circle that touches the side \(BC\) of triangle \(ABC\) at point \(B\) and passes through point \(A\) lies on segment \(AC\). Find the area of triangle \(ABC\), given that \(BC = 6\) and \(AC = 9\).

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