
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 \(ABC\), where \(AB = BC = 6\) and \(AC = 2\), the median \(AA_1\), the altitude \(BB_1\), and the angle bisector \(CC_1\) are drawn. Find the area of the triangle formed by the intersection of the lines:
a) \(BB_1\), \(CC_1\), and \(BC\); 
b) \(AA_1\), \(BB_1\), and \(CC_1\).

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