
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
Triangle  $ABC$  has  $AB=BC=10$  and  $CA=16$ . The circle  $\Omega$  is drawn with diameter  $BC$ .  $\Omega$  meets  $AC$  at points  $C$  and  $D$ . Find the area of triangle  $ABD$ .

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