
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  $I$  and  $O$  be respectively the incentre and circumcentre of a triangle  $ABC$ . If  $AB = 2$ ,  $AC = 3$  and  $\angle AIO = 90^{\circ}$ , find the area of  $\triangle ABC$ .

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