
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 an acute triangle \(ABC\), the altitudes intersect at point \(H\), and the medians intersect at point \(O\). The angle bisector of \(\angle A\) passes through the midpoint of the segment \(OH\). Find the area of triangle \(ABC\) if \(BC = 2\), and the difference between angles \(B\) and \(C\) is \(30^\circ\).

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