
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 a line passing through the center $O$ of a circle with radius 12, points $A$ and $B$ are chosen such that $OA=15$, $AB=5$, and $A$ lies between $O$ and $B$. Tangents are drawn from points $A$ and $B$ to the circle, with the points of tangency lying on the same side of the line $OB$. Find the area of triangle $ABC$, where $C$ is the point of intersection of these tangents.

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