
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 $C$ and $C^{\prime}$ be two externally tangent circles with centers $O$ and $O^{\prime}$ and radii 1 and 2, respectively. From $O$, a tangent is drawn to $C^{\prime}$ with the point of tangency at $P^{\prime}$, and from $O^{\prime}$, a tangent is drawn to $C$ with the point of tangency at $P$, both tangents being in the same half-plane relative to the line passing through $O$ and $O^{\prime}$. Find the area of the triangle $O X O^{\prime}$, where $X$ is the intersection point of $O^{\prime} P$ and $O P^{\prime}$.

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