
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
In the new diagram, suppose $\overrightarrow{OA}\perp\overrightarrow{OC}$ and $\overrightarrow{OB}\perp\overrightarrow{OD}$ just as previous problem suggested. However, now $\angle{AOD}$ is 2.5 times $\angle{BOC}$. Find the measure of $\angle{AOD}$.

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