
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
Two circles are constructed on a plane in such a way that each passes through the center of the other. Points $P$ and $Q$ are the points of their intersection. A line passing through point $P$ intersects the first circle at point $A$ and the second circle at point $B$ such that $P$ is between $A$ and $B$. This line makes an angle of $15^{\circ}$ with the line connecting the centers. Find the area of triangle $ABQ$ if it is known that $PQ = 2\sqrt{3}$.

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