
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 extension of side \( AC \) of triangle \( ABC \), whose area is \( S \); point \( A \) is between \( D \) and \( C \). Let \( O \) be the centroid of triangle \( ABC \). It is known that the area of triangle \( DOC \) is \( S_l \). Express the area of triangle \( DOB \) in terms of \( S \) and \( S_l \).

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