
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
Point \( D \) lies on the side \( AC \) of triangle \( ABC \). A circle with diameter \( BD \) intersects sides \( AB \) and \( BC \) at points \( P \) and \( T \) respectively. Points \( M \) and \( N \) are the midpoints of the segments \( AD \) and \( CD \) respectively. It is known that \( PM \| TN \).

a) Find the angle \( ABC \).

b) Additionally, it is known that \( MP = 1 \), \( NT = \frac{3}{2} \), and \( BD = \sqrt{5} \). Find the area of triangle \( ABC \).

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