
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 \( O \) is located on side \( AC \) of triangle \( ABC \) such that \( CO : CA = 2 : 3 \). When this triangle is rotated by a certain angle around point \( O \), vertex \( B \) moves to vertex \( C \), and vertex \( A \) moves to point \( D \), which lies on side \( AB \). Find the ratio of the areas of triangles \( BOD \) and \( ABC \).

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