
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
A *3-4-5 point* of a triangle  $ ABC $  is a point  $ P $  such that the ratio  $ AP : BP : CP $  is equivalent to the ratio  $ 3 : 4 : 5 $ . If  $ \triangle ABC $  is isosceles with base  $ BC = 12 $  and  $ \triangle ABC $  has exactly one  $ 3-4-5 $  point, compute the area of  $ \triangle ABC $ .

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