
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 $\boldsymbol{D}$ lies on the extension of side $\boldsymbol{A} \boldsymbol{C}$ of triangle $\boldsymbol{A B C}$, whose area is $\boldsymbol{S}$, with point $\boldsymbol{A}$ situated between $\boldsymbol{D}$ and $\boldsymbol{C}$. Let $\boldsymbol{O}$ be the point of intersection of the medians of triangle $\boldsymbol{A B C}$. It is known that the area of triangle $\boldsymbol{D O C}$ is $\boldsymbol{S}_{I}$. Express the area of triangle $\boldsymbol{D O B}$ in terms of $\boldsymbol{S}$ and $\boldsymbol{S}_{I}$.

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