
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

In triangle \(ABC\), the angle bisector of the angle at vertex \(A\) intersects side \(BC\) at point \(M\), and the angle bisector of the angle at vertex \(B\) intersects side \(AC\) at point \(P\). The angle bisectors \(AM\) and \(BP\) intersect at point \(O\). It is known that triangle \(BOM\) is similar to triangle \(AOP\), and \(BO = (1 + \sqrt{3}) OP\), \(BC = 1\). Find the area of triangle \(ABC\).

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