
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
Let $O$ be the point of intersection of the medians of triangle $ABC$ and $\overline{AO} = \bar{a}, \overline{AC} = \bar{b}$. Decompose $\overline{AB}$ and $\overline{BC}$ into vectors $\bar{a}$ and $\bar{b}$.

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