
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 \(ABC\), side \(BC\) is equal to 6, side \(AC\) is equal to 5, and the angle at vertex \(B\) is \(30^\circ\). Find the area of the triangle if the distance from vertex \(A\) to line \(BC\) is less than \(\frac{1}{\sqrt{2}}\).

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