
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
On the coordinate plane, a circle with center \( T(3,3) \) passes through the origin \( O(0,0) \). If \( A \) is a point on the circle such that \( \angle AOT = 45^\circ \) and the area of \( \triangle AOT \) is \( Q \) square units, find the value of \( Q \).

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