
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
A circle constructed with side \( AC \) of triangle \( ABC \) as its diameter passes through the midpoint of side \( BC \) and intersects side \( AB \) at point \( D \) such that \( AD = \frac{1}{3} AB \). Find the area of triangle \( ABC \), given that \( AC = 1 \).

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