
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 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 segments \( AD \) and \( CD \) respectively. It is known that \( PM \parallel TN \).

a) Find the angle \( ABC \).

b) Additionally, it is given that \( MP = \frac{1}{2} \), \( NT = 1 \), and \( BD = \frac{4}{3} \). Find the area of triangle \( ABC \).

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